One way to put together the adjudication section of the report

Step one:
  Cut and paste the previous turns ending position to the new report.
 
This example is taken from 370 the Fall 1904 turn.  A game I took over at this point and had to readjudicate because of several errors in the adjudication.
Austria:  A Bul, A Rum, A Bud, A Ser, F Aeg.
England:  F Ber, F Nth, F Den, F Edi, A Wal.
France:   F Tun, F Nap, A Ven, A Bel, F Eng, A Mun.
Germany:  A Kie, A Ruh, A War.
Italy:    F Eas, A Rom, F Ion, F Tyl, A Tri.
Russia:   F Swe, F Nwy, A Mos, A Ukr, A Stp.
Turkey:   F Bla, F Con, F Smy, A Sev.

 
Step two:
  Paste the orders sent from the players into the starting positions for the turn, one order at a time.  Annotate any extra, missing or double orders as failing or holding.
 
At this point I normally change their orders into my abbreviation set as well.  You may choose to post the orders the way you receive them.  Normally, I run the orders horizontal.   However, in this example I will run them vertical.  These types of decisions are up to you.  Use whatever works best for you.  I'm also going to show the orders the way I received them.
Austria: 
A-Bulgaria S A-Rumania
A-Rumania S RUSSIAN A-Ukr.-->Sev.               
A-Budapest S A-Rumania                  
A-Serbia S A-Bulgaria
F-Aegean S ITALIAN F-East Med.-->Smyrna

England: 
F-Berlin-->Baltic Sea
F-North Sea S F-North Sea
F-Denmark S F-North Sea
F-Edin-->York
A-Wales ST

France:  
F-Tunis ST
F-Naples S A-Venice-->Rome                      
A-Venice-->Rome                                 
A-Belg. ST
F-Eng. Channel S A-Belgium
A-Munich S GERMAN A-Kiel                      

Germany: 
A-Kiel-->Berlin                                 
A-Ruhr-->Munich                               
A-Warsaw-->Prussia                              

Italy:
F-East Med.-->Smyrna 
A-Rome S F-Ionian-->Naples                      
F-Ionian-->Naples                            
A-Tyrolia-->Venice
A-Treiste S A-Tyrolia-->Venice

Russia:  
F-Swe ST
F-Norway ST
A-Moscow S A-Ukr.-->Sevastopol
A-Ukr.-->Sev.
A Stp ST ?                               Unordered

Turkey:  
F-Blk. Sea-->Rumania 
F-Const. S F-Smyrna
F-Smyrna S F-Const.
A-Sevastopol ST

Note we had one Unordered piece. Above I marked it Unordered.

This is how it would look, at this point if I were doing it.  I translate the moves to my abbreviations and remove unnecessary text like the Foreign country names, etc.  Using my format I follow unordered pieces with (u).  Should I have difficulty in translating a move than it's a poorly written order, shown in its received format and marked as unknown or ambiguous.

Austria: A Bul S Rum, A Rum S Ukr-Sev, A Bud S Rum, A Ser S Bul, 
         F Aeg S Eas-Smy.
England: F Ber-Bal, F Nth h, F Den S Nth, F Edi-Yor, A Wal h.
France:  F Tun h, F Nap S Ven-Rom, A Ven-Rom, A Bel h, 
         F Eng S Bel, A Mun S Kie.
Germany: A Kie-Ber, A Ruh-Mun, A War-Pru.
Italy:   F Eas-Smy, A Rom S Ion-Nap, F Ion-Nap, A Tyl-Ven, 
         A Tri S Tyl-Ven.
Russia:  F Swe h, F Nwy h, A Mos S Ukr-Sev, A Ukr-Sev, A Stp h(u).
Turkey:  F Bla-Rum, F Con S Smy, F Smy S Con, A Sev H.

 
Step three
  Execute the orders and determine the outcome using a board and either the rules or the DPTG.  I use a set of rules (1976) you may only have the DPTG available to you.  You do it enough times, you won't need a map or board to perform the task.  One of reasons I use my concise format is that I can usually see all the orders in a small space and mark bounces and cuts rather quickly.

 
Step four:
  Annotate the orders that failed indicating how they failed (Invalid, cut, bounce, dislodged, annilated, etc.)
 
Austria: 
A-Bulgaria S A-Rumania
A-Rumania S RUSSIAN A-Ukr.-->Sev.       Cut by Black Sea
A-Budapest S A-Rumania                  
A-Serbia S A-Bulgaria
F-Aegean S ITALIAN F-East Med.-->Smyrna

England: 
F-Berlin-->Baltic Sea
F-North Sea S F-North Sea
F-Denmark S F-North Sea
F-Edin-->York
A-Wales ST

France:  
F-Tunis ST
F-Naples S A-Venice-->Rome              Cut by Ionian Sea
A-Venice-->Rome                         Bounces 1v1, Dislodged by Tyrolia 2v1, 
                                        Retreat Required
A-Belg. ST
F-Eng. Channel S A-Belgium
A-Munich S GERMAN A-Kiel                Fails, Kiel ordered to move, Cut by Ruhr

Germany: 
A-Kiel-->Berlin                              
A-Ruhr-->Munich                         Bounces 1v1
A-Warsaw-->Prussia                              

Italy:
F-East Med.-->Smyrna                    Bounces 1v1
A-Rome S F-Ionian-->Naples              Cut by Venice
F-Ionian-->Naples                       Bounces 1v1
A-Tyrolia-->Venice
A-Treiste S A-Tyrolia-->Venice

Russia:  
F-Swe ST
F-Norway ST
A-Moscow S A-Ukr.-->Sevastopol
A-Ukr.-->Sev.
A Stp ST ?                              Unordered

Turkey:  
F-Blk. Sea-->Rumania                    Bounces 1v1
F-Const. S F-Smyrna
F-Smyrna S F-Const.                     Cut by East Med
A-Sevastopol ST                         Dislodged by Ukrania 2v1, Retreat required

Here is how it looks doing it my way.

The squared brackets means the move fails.  I don't make distinctions between bounces and cuts.  If it tried to move and it has square brackets, its a bounce, if its supporting something and it has square brackets the support was cut.  The rounded brackets are where I place additional comments.  In my notation I use ATT means that the piece has been attacked and dislodged.  I don't use "D" alone to mean Dislodged because it could mean Disbanded.  The OTM means simply that the piece was ordered to move.  The r-? means I need a retreat.  Had the piece been Annihilated, it would have been shown as ATT:ANN.  A copy of the this notation can be found here.

Austria: A Bul S Rum, [A Rum S Ukr-Sev], A Bud S Rum, A Ser S Bul, 
         F Aeg S Eas-Smy.
England: F Ber-Bal, F Nth h, F Den S Nth, F Edi-Yor, A Wal h.
France:  F Tun h, [F Nap S Ven-Rom], [A Ven-Rom(ATT:r-?)], A Bel h, 
         F Eng S Bel, [A Mun S Kie(OTM)].
Germany: A Kie-Ber, [A Ruh-Mun], A War-Pru.
Italy:   [F Eas-Smy], [A Rom S Ion-Nap], [F Ion-Nap], A Tyl-Ven, 
         A Tri S Tyl-Ven.
Russia:  F Swe h, F Nwy h, A Mos S Ukr-Sev, A Ukr-Sev, A Stp h (u).
Turkey:  [F Bla-Rum], F Con S Smy, [F Smy S Con], [A Sev H(ATT:r-?)].

 
Step five:
  Recheck situations you are unsure about.  If uncertain ask for advice from the GM List.
 
The previous GM dislodged the French Fleet.  I don't recall what the argument was but I could guess that he concluded that since the Venice piece was dislodged it couldn't cut the support of Rome and therefore the Ionian move to Naples succeeded.  This of course isn't true.  At any rate in my readjudication the error turned up and I made it point in the report to annotate any differences and provide justification.  The following was my notation.

The French Fleet remains in Naples. Army Venice though dislodged still
cuts the support of Rome to the Ionian Fleet moving to Naples.  Its also
true that the Fleet Ionian sea cut the support for Army Venice to Rome
from Fleet Naples.  Hence, France owns Naples as well, because it
occupies it in the fall.
This is a complex enough situation where a predural comment might be in order like this one.  This turn was adjudicated by the original GM and did end up with discussion afterwards on the GM list.  The GM opted to give up the game, I took over and readjudicated the turn.

 
Step Six:
  Record the ending position.  This provides a place to cut the paste the starting positions from, for the next turn.  It also provides the player with a means of setting up the board without reading through the adjudication should a map be unavailable.

 
I will only show my version of it here.

Austria:  A Bul, A Ser, A Rum, A Bud, F Aeg.
England:  F Nth, F Yor, F Den, F Bal, A Wal.
France:   F Tun, F Nap, A Ven, A Bel, F Eng, A Mun.
Germany:  A Ber, A Ruh, A Pru.
Italy:    F Eas, F Ion, A Rom, A Ven, A Tri.
Russia:   A Stp, A Sev, A Mos, F Swe, F Nwy. 
Turkey:   F Con, F Smy, F Bla, A Sev.

Please note:  That even though Venice and Sevastipol have been dislodged the pieces are still shown in this report.  The reason for this is because we have not received retreats and its the only appropriate to show it.  I use this section to generate my maps.  showing it like this also allows me to show it on the map.

 
Step seven:
  Request any retreats needed, adjudicate them.
 
This is how I request retreats. Note:  I don't tell the player what spaces are available, but if none are available I do show the piece as annhilated.  Knowing where you can retreat is as much a part of the game as submitting orders to the GM.
Adjustments Needed:
France:  Retreat: A Ven.
Turkey:  Retreat: A Sev.
When I get them back I update the fall report to show where the pieces where retreated.  I update it in my adjustments section, I replace the ?'s with the location and I update the ending position.

Adjustments:
France:  Retreat: A Ven-Tus.
Turkey:  Retreat: A Sev-OTB.

Note:  OTB stands for Off-The-Board which is always a valid move for a retreat.

 
Step eight:
  Determine any needed builds and disbands undating the supply center table if its a Fall/Winter turn.
 
Most of the comments about this game were about supply center counts.  When I took over I had to research who owned what centers.  I make it my practice to include the supply center table in every report.  Though it only gets updated after the Fall retreat phase.  It is what shows who owns what and it rarely matches the board set up.  By doing so it keeps everything together.

Supply Centers (before updating)
--------------
Austria(5):  Bud, Tri, Ser, Bul, Gre.
England(5):  Lon, Edi, Lpl, Den, Kie.
France(6):   Par, Mar, Bre, Spa, Por, Bel.
Germany(3):  Ber, Mun, Hol.
Italy(5):    Rom, Ven, Nap, Tun, Vie.
Russia(5):   Mos, War, Stp, Nwy, Swe.
Turkey(5):   Con, Smy, Ank, Sev, Rum.


Supply Centers (after updating)
--------------
Austria(5+1-1=5):  Bud, /Tri/, Ser, Bul, Gre, *Rum*.
England(5+0-0=5):  Lon, Edi, Lpl, Den, Kie.
France(6+3-0=9):   Par, Mar, Bre, Spa, Por, Bel, *Tun*, *Nap*, *Mun*.
Germany(3+0-1=2):  Ber, /Mun/, Hol.
Italy(5+1-2=4):    Rom, Ven, /Nap/, /Tun/, Vie, *Tri*.
Russia(5+1-0=6):   Mos, War, Stp, Nwy, Swe, *Sev*.
Turkey(5+0-2=3):   Con, Smy, Ank, /Sev/, /Rum/.
I use the /'s to mark lost centers and the *'s to mark gained centers.

Next you compare the number of centers to the number pieces and request adjustments accordingly. Hence, the adjustment section would look as follows:

Adjustments Needed
------------------
France:   Build: 3.
Germany:  Remove: 1.
Italy:    Remove: 1.
Russia:   Build: 1.

Plese note that no adjustments for Turkey were requested because he was already playing short and he removed A Sevastipol during the retreat phase.  Had the retreat phase been combined with the building and disband phase like I do I would have shown Turkey as needing to Remove a piece as well.

The following notes show how messed up this section was when I took over and it serves to emphasize the need to have it present on all reports.

England owns Kie, not Germany.  The Fall 1903 report shows the ownership
of Kiel by England, The Spring 1903 moves show that England moved a
piece from Kiel. In the Fall 1904 Kiel is unoccupied, therefore it
remains England's.  Ownership passes with occupation in the Fall.

Germany owns Hol, not England.  The Fall 1903 report shows the ownership
of Holland by Germany, the Winter 1903 Builds and Removals show that
Germany disbanded Holland.  Holland is not occupied this Fall and is
therefore Germany's.

Germany's Prussia was shown as disbaned.  It was not forced to retreat
and therefore can not be retreated off the board during the retreat
period.  Prussia will be assumed to be the piece removed by Germany
during the Winter turn should I not here from him and his adjustments
are all that are missing.  Should he decide to disband differently he
may.

Russia owns Warsaw, not Austria.  Russia owned it last Fall, moved out
in the Spring while Germany moved in made himself at home there and in the
Fall Germany moved out of Warsaw.  Since, Warsaw is not occupied this
Fall its previous owner stills owns it and that is Russia.
I'm GM'ing. What do I do?

 
Step nine:
  Obtain the adjustments, place the units and update the final position.
 
In game 370, it would have looked like this after posting.

Winter Adjustments
------------------
France:   Build: F Bre, A Mar, A Par.
Germany:  Remove: A Pru.
Italy:    Remove: A Tri.
Russia:   Build: A War.

Final Position after adjustments
--------------------------------
Austria:  A Bul, A Ser, A Rum, A Bud, F Aeg.
England:  F Nth, F Yor, F Den, F Bal, A Wal.
France:   F Tun, F Nap, A Tus, A Bel, F Eng, A Mun, 
          F Bre, A Mar, A Par.
Germany:  A Ber, A Ruh.
Italy:    F Eas, F Ion, A Rom, A Ven.
Russia:   A Stp, A Sev, A Mos, F Swe, F Nwy, A War. 
Turkey:   F Con, F Smy, F Bla.
Some notes before moving on.