The answers to the crossword puzzle:
       
WADI.GRO.ABSORB.TAZ.LAX
OMEN.HAD.RESHOE.IVE.EVE
NICKNAME.GERMAN.MESSIER
...YEN..MOP..ROBERTO...
TOP.WALDO.EES.IRS..HULA
UNITS.INTERSTATE.ATOMIC
GONG.SPAIN.LUC.AVIS.PET
...VEEP.FDR.BIB.IMAC...
GOO.KEYS.OAR.DAWNS.OAFS
NUMBER.COWPARSLEY.ASCII
URGE..RAT.TWA.SELIG.HEX
...ARMENIA..NBA..DOW...
REQUIEM.OBJECT.NEIGHBOR
ORE.PTA.SEEYOU.AGO.AIDA
ZED.ASP.ELDERS.POM.MODE

The missing number in the puzzle, as emphasized in 111-Down, the penulitmate clue, is 45. In fact, the clue numbers skip from 44 to 46, in part because I didn't want to confuse you in the next step, when 45 is to be used literally in the clues, and not as a key into the crossword puzzle!

Replacing the numbers with their answers, and inserting "45" into each clue, gives:

HEX         ASCII       45
VEEP        45          NICKNAME
VINYL       45          UNITS
___ 45:     GERMAN      REQUIEM
INTERSTATE  45          NEIGHBOR
METS        45          TUG
ATOMIC      NUMBER      45
MESSIER     OBJECT      45

Which give the answers:

E         
AL        
RPM       
OPUS      
TEXAN     
MCGRAW    
RHODIUM   
PLEIADES  

Transferring letters, we find that the quip begins..

"HE THOUGHT HE WAS A WIT -- AND HE WAS

and the final clue is:

45  DEGREES, PERHAPS

which, combined with the depicted triangle and the context, completes the quip:

"HE THOUGHT HE WAS A WIT -- AND HE WAS __HALF__RIGHT__"

The inspiration was

XI MAR MCMLXIX

or 11 Mar 1969, the day I was born. This puzzle was constructed to celebrate my 45th birthday.