This wasn't a problem a few days ago, but now I can't run the game with Tribunal and Bloodmoon. I get error messages along the lines of "Chunk size 10 too big in chunk WEAT_ID" and a bunch of other stuff like that. If I play without the plugins, my game works just fine. Any suggestions? I need the expansions working again, as half of my mods depend on it.

Looks like you installed the expansions in the wrong order.
It needs to be: MW-Tribunal->Bloodmoon
No need to uninstall anything, a simple re-install of Bloodmoon should fix your problems.

The games starts, but when I get to the census office, I get a "Mesh-load error: meshes/gtj/gtj_water_mesh.nif cannot load file.

That file doesn't exist in the standard game.
Looks you installed a mod incorrectly, or the mod is missing that file.