Hopefully someone else will chime in if I forget something, but usually you'll want to visually inspect the bass:
Sight down the neck and see if its twisted or has a weird bend to it (Something not correctable by a truss rod adjustment...looks like a rolercoaster with bumps, etc. I'm not talking about normal relief).
Check the frets to see if they are in good condition...don't have sharp edges coming out of the side of the fretboard that will cut you and aren't worn down.
Check the neck/body joint to make sure that the neck is aligned properly. Pay particular attention for an excessive gap between the body and neck.
Check the body and neck for damage. Cracks, chips, scrapes, etc... Cosmetic damage is one thing, actual functional damage is another entirely.
Check the truss rod and make sure it works. If you don't know how to do this take a look at the sticky section in the setup section here on TB.
Check the tuners and make sure they are attached solidly and turn without binding.
Plug in the bass and check all the knobs, switches and jack. Turn all the knobs and switches one at a time and listen for static, distortion or popping. Make sure everything works. Make sure everything feels solid.
With the bass plugged in, play each note on the neck individually to check for dead spots and bad/uneven frets.
Finally check anything else you can think of. How the screws holding on the bridge and pickguard are sunk into the bass (are they straight or crooked?). How the pickguard is aligned (does it look like it was put on correctly?). Check the bridge. Make sure its centered correctly. If not the strings will be off-centered on the fretboard. Are the inlays on the neck smooth with the fretboard? Is there excessive glue visible around them? Does the nut look good? Etc...
Hope that helps.
