Христос воскрес really is a borderline case since it's correct Russian.
As for actual "mistakes" — let's first establish what we consider a mistake. I'm going to disregard popular prescriptivist tics such as the crusade against одеть пальто (insisting on надеть пальто), and other examples that are considered jarring and "uncultured" on the questionable premise that everyday language is a thing that can and should be regulated. Let's limit ourselves with those cases where the speaker is clearly aiming for the formal/literary register while breaking some of its expected norms.
A lot of such mistakes have to do with misplaced stress, such as дóговор instead of договóр, and with oblique cases of large numerals: by far not all native speakers will get through тысячей семьюстами шестьюдесятью without stumbling or using the wrong ending somewhere.
Others are more specific:
Не instead of ни in "whatever/whoever/wherever" constructions. Since they sound the same except in one case, with the past tense of быть, this mostly only results in spelling mistakes, but you do also get что бы это нé было instead of что бы это ни было.
Lack of agreement of verbal adverb phrases with the subject of the main clause. Often exemplified with Проезжая мимо станции, с меня слетела шляпа (a shortened and slightly paraphrased quote from a story by Chekhov, where it's used deliberately for comedic effect.)
A duplicate бы somewhere down the line in a long subordinate clause that already began with чтобы.
Обоих/обоим where обеих/обеим is expected.
Similar to the previous item: using the forms двое, трое, etc. with female-only groups. (Not currently a prominent part of our gendered language debates that I'm aware of, but one can certainly expect calls for retiring this distinction at some point. For now, it's bad grammar.)
Genitive instead of dative with согласно "according to".
Just the ones I could think of off the top of my head; I don't also want to veer into what's no longer issues of pure grammar rather than style, such as people mixing up неприкасаемый and неприкосновенный, or arguing whether другая альтернатива is or isn't a tautology.