It really depends on whether it was fixed professionally or by some dude in his garage. Generally if people buy the car back from their insurance company after it was totalled they do the work themselves and don't usually do a really good job. SOMETIMES you get an edge case where the value of the car was low to begin with so even with comparatively minor damage the insurance company can total it out.
So here are the things you may run into with a salvaged car:
severe body damage that has been fixed with bondo and painted over -- basically, the body of the car can fall apart easily, rust can form underneath, etc.
air bag deployments -- if the airbags deployed it's really expensive to put them back so people just cut them out and put it back together -- it means if you get in a wreck no airbags are there anymore
bent frame -- look at all the joints between all the body pieces, they should have even gaps. Look at the tires, if they are brand new that may be a bad sign because they may be covering up alignment problems that can't be fixed because the frame is tweaked (if tires can't align, you get severe uneven wear and end up burning through tires in just a couple hundred miles)
Look at all the window and door seals, you can also get misaligned or leaky windows which allow water to come into the car -- even if it's just a drop every now and again if it makes its way behind the dash onto any electrical components you're screwed.
If it wasn't from a wreck, but instead flood or storm damage, you can get severe electrical issues, mold growth, bad smells, etc. If there are any strong air fresheners in the car they are trying to cover something up.
You really should have a mechanic look it over, but for a cursory inspection I'd look for:
bad body/paint work
smells
shaky brakes
weird noises from engine, transmission, drivetrain
doors that don't open/close properly
windows that don't open/close properly
uneven wear on tires
dirty/dingy oil
dark (not bright red) transmission fluid (might also smell burnt if it's bad)
coolant not in good condition; if it's not bright green or bright orange it hasn't been maintained properly
when you're testing driving, make sure there are no weird knocks or shakes, especially going around corners (can indicate transaxle issues) or hitting bumps (other suspension issues like shocks/struts, sway bars, u-joints, ball joints, etc.)
Also get a carfax, it may have some more information on why it was totalled. It also might tell you the original state of origin so if it was licensed, for example, in New Orleans during the hurricane, run away.