Mostly pronunciation. Palatalization. How to pronounce the letters И and Ы and O. Stress positions (in many words stress falls on different syllables depending on grammatical case for nouns and person in verbs). Sentence intonation patterns. But basically, you don't know what you don't know, but a tutor will know.

I remember the first time I saw a Polish newspaper (I'm from Chicago, the second-largest city of Polish speakers!) I wondered how to pronounce the word w. That was before I learned Russian.