During many years it was rather difficult to check the spelling of LATEX sources written in Romanian.
Fortunately, the rospell project is now sufficiently mature. You can download from its page dictionaries for GNU Aspell.
GNU Aspell is included in many Linux distributions.
On Windows one may use the GNU Aspell Win32 version or FreeSpell, which uses the Aspell engine. FreeSpell has the advantage that you can check only the selected text. It works well with Vim under Windows and this is all you need for LATEX .
For details, see my new notes on the Romanian dictionaries for GNU Aspell.
I have also some old notes on the same topic (with screenshots).