Judging a bicycle show
Some things i would consider, some could possibly be grouped together. Perhaps others can add on with more answers.

Custom Class


Originality/Creativity
Function 
*Can you actually ride it semi comfortably or is it just cool looking
*Can it do something normal bikes can't?
Use of colors or materials (could lump into creativity)
Wow factor
Overall theme 


Vintage Class


Period correctness (50's era components on a 50's era cycle)
Original parts (as much as possible)
Cleanliness
Paint/Chrome quality (new or original)
Function (are all required parts present and in working order)


For your points system, decide on what things you would like to judge , using my list as an example you could give each a 20 point value, 5 topics totaling 100 points maximum - Highest score wins