We'll assume, for the purposes of this question that you're looking for the vintage screwback models such as the DW-5000, WW-5100, DW-5200, WW-5300, DW-5400, DW-5600, DW-5700 or DW-5800. These models all utilize the same case/bezel/module configuration with some differences. Here are a few things to look for:
Crystal - if the crystal is cracked or very badly damaged then consider the watch a parts watch and bid accordingly. Crystals for vintage G-Shocks are very difficult to find, will be expensive to purchase and are tricky to install properly.
Bezel screws - if one of these is broken off inside the case proceed with caution. They can be removed but with some difficulty. If the bezel screws are missing consider that only the Phillips head screws (for the DW-5600, DW-5700, and DW-5800) are available as replacements. Slot head screws (as on the DW-5000, WW-5100, DW-5200, WW-5300, and DW-5400) are no longer available and the gold screws will be very tough to locate.
Modules - the modules 240, 491, 691 and 901 are robust and will usually come back to life with a new battery so buying 'dead' watches should not be a concern. That said, be aware that the module 491 (found on the WW-5100 and WW-5300) occasionally has a fault which causes the stopwatch, timer and alarm to display all 8's. Also, the module 491 does not have a light.
If the light on your module is weak or does not work there is likely nothing you can do to fix it, provided the battery has already been changed.
If the module appears to be sitting crooked in the case it is a simple matter to open up the case and move the module around with your fingers until it is seated correctly.
The modules 691 and 901 will 'beep' as you scroll through the Modes but the 240 and 491 do not 'beep' when the Mode button is pressed.
Bezels - replacement bezels are available for the DW-5000, WW-5100, DW-5200, WW-5300, DW-5400, DW-5600 and DW-5800 - these all use the same square bezel.
The DW-5400 and DW-5700 each use a round bezel which is no longer available and will be difficult and expensive to source. The correct bezel for the DW-5400 has '24HR' at the lower right and the correct bezel for the DW-5700 has 'REM' at the lower right.
If the model is one of the 'gold' versions (gold colored buttons, gold accents on the dial) then the bezel will have gold lettering.
Bands - all the models listed above use the same band and replacements are available. If the watch is a 'gold' version then the buckle will be gold as well.