This is interesting question.
I'm sorry to post here, but I'd like to share my experience.
I do speak three languages fluently, and those three are from different language categories; Japanese, Indonesian, and English. I also understand Hawaiian, but not as fluent as other three.
In my opinion, grammatical mistakes are more based on the educational background on the language, but are not caused by multilingualism. Most monolingual people make more grammartical mistakes than I do, in my experience.
Actually, English is my third language, but because I have had the most intensive training on English grammars, I'm confident when I write/read/speak in English more than other two.
And, most people never care about how correct the grammar is, when they are just chatting.