I'm hoping to make this a running thread of known (in)compatibilities with BGEE. A lot of this at the beginning will be, unfortunately, trial-and-error and a lot of updating by mod authors. If you should find a problem with a mod, let fellow players know here but more importantly let the mod author know. Mods have readmes with contact information; the mod will never be fixed unless the author is at least aware of the issues. I'll start us rolling with my own stuff below.
Since BGEE is essentially BG1 content in the BG2 engine, which mod may be appropriate is often unclear, e.g. you should use BG2 Tweaks on BGEE, not BG1 Tweaks.