Hard to really say, since there are soooooo many different types of corals out there. Yes... bleached is an obvious one and you're right, it means they're pretty much white, or very very pale. Corals can bleach for numerous reasons and is a good warning sign to leave that one at the LFS
I'm mostly an LPS
guy, so that's what my comment apply to...
Exposed skeleton is one to avoid, but that's hard to know what you're looking at when you're first starting. What comes to mind for me is Bubble Corals were the sharp septa (the underlying skeleton) are poking through the tissue.
On branching type LPS
corals (like anchor, torch, frogspawn, duncans, etc) you want corals that have a fair amount of tissue going down the base of the stalk, or skeleton. You don't want the living tissue just hanging on by a little bit at the tip of the skeleton. Also, where the living tissue ends on the skeleton, look for obvious recession. If you can see a portion of white skeleton (not yet discolored or covered in coraline algae) directly below the living tissue, that means the tissue has receded recently, or is in the process of receding. Obvious recession is something I stay away from.
Good expansion is good to look for, but if it isn't present it doesn't mean the coral isn't healthy. It could still just be acclimating, or doesn't like the lighting it's under, or is under too much flow. Open Brain Corals (Trachyphillia) come to mind - seems like they're always closed up tight at the LFSs.
I avoid corals that have obvious algae on the skeleton or attached rock. Yeah... you can pick it off, but you rarely get it all. And then it's forever in your tank! Flatworms are another thing to look for on LPS
. Again... hard to see when you're first starting out, but once you buy a coral with them, you'll know what to look for! (It *will* happen if you stay in the hobby long enough!)
These are things off the top of my head, and I'm sure I've missed a ton of things. Best advice is to get a good book on corals (Eric Borneman's "Aquarium Corals" is my favorite 'start here' book) and read read read. And look at the pictures! Also... visit different LFSs frequently and just look. Over time, you'll start to notice the subtle differences between great corals, and so-so pieces.
[Edit: Another that came to mind are Favia and Favite corals that have portions of them damaged from localized trauma (rockfall, clumsy crab, etc) or from an attack from a neighboring coral. The coral definitely has the ability to heal itself from that injury, but at the same time it's an easy path for disease to enter. Unless you are comfortable fragging (cutting) away that portion of damaged coral, it's probably best to leave those at the LFS
too. Seems like more times than not, when I'm watching a specific coral at a LFS
damaged like this, they usually get worse... not better.]