Does the following sentence contain any grammatical errors?

Those are the kinds of people whom I will never talk to.

Thanks, Leo

Although it ends with a preposition, which some purists consider poor form, I see nothing wrong with the sentence. It also used "whom" correctly instead of "who". The plural verb "are" also correctly goes with the plural subject "those...kinds".

"Whom" is being used as a relative pronoun to link clauses. That is also perfectly OK.

Those are the kinds of people whom I will never talk to.

If you want to make this sentence perfectly correct to meet the standards of purists, you could say --
Those are the kinds of people to whom I will never talk.

However, that is awkward. The simplest way of expressing that idea is --
I will never talk to those kinds of people.

No, the original sentence does not contain any grammatical errors.