I have spellChecking = 1 in my .tm_properties file, and this works very well for LaTeX projects. In particular, it shows errors that are already there when I load files, and highlights any new errors that I type.
Indeed. But I was enabling spell checking via menu, and there was no effect on already loaded document.
However following your suggestions, when spell checking was already enabled in tm_properties, the errors were marked correctly upon load.
Using the spelling settings in the menus doesn't seem to work very well though - and this is probably one of those "we recommend you put settings in .tm_properties files for the moment, as some things don't stick if you use the menus".
Hmmm... it seems that I would need to fiddle with tm_properties then, as changing the language when TM is running is broken. At least when I have several files in multiple languages.