A full lists of "don'ts" would be incredibly long--soo many species of trees out there and a lot of folks really don't know how to id living trees accurately, much less id fallen or water-logged bits they find.
Your best bet is to stick with wood specifically sold for aquarium use or marked as safe for aquariums (manzanita and mopani are both often used for reptile use, if you check the hang tag you'll often find a small blurb about being safe for aquarium use also). Grape"wood" is often found in reptile/bird sections and I've yet to see a definitive answer on how well it stands up to aquarium use--some say it disintegrates too quickly, others claim it's fine.
Past that, you'll want to stick with hardwoods (shouldn't be able to make a dent in it with your fingernail) that have been thoroughly dried or which are harvested from waterways already having become waterlogged over time. As with anything harvested from nature, thorough cleaning is a must to avoid introducing unwanted elements--biological or chemical--to your tanks.