I think it is important to differentiate between what sound "wrong"(=uneducated) and "wrong" (=non-native).
I've made a little list (excluding medieval grammarians' inventions like split infinitive) of expressions that sound wrong (at least to some), but not non-native, and made notes of how I, personally, perceive these. I am sure others feel differently, so I'd love to hear comments on that:
1. ain't, double negatives, messed conjugation ("we was"): definitely wrong.
2. Messing objective and direct cases: "Between you and I", "Who's there? - Мe". The former makes me cringe, the latter not so much.
3. Using who instead of whom - basically a norm now; using whom instead of who - I find it unacceptable
4. Confusing farther and further - sounds wrong, but not terribly so.
5. Try and //verb//, instead of "try to //verb//" - OK
6. Like better, instead of like more - perfectly OK
7. Confusing "that" and "which", like in "Conclusions were spelled out in the summary that/which was attached to the report". Formally, the meaning is different (and one demands a comma and the other doesn't), but people routinely confuse them. I accept, but do not like this.
What else did I miss? Yesterday's colloquialisms becoming grammatical norms today?