Should a reviewer critique language and text copy-paste issues? While reviewing research papers, I often find that the author's English is not very good. Considering that English is not everyone's native language, I understand their difficulties, and I recognize that they struggle (using dictionaries and translators) to get their work published at all.

That being said, I sometimes find papers that have contain English that is frankly terrible, with a few select fragments in pristine, almost Shakespearean English, using words that sometimes I didn't even know existed. When this happens, a quick Google search will occasionally reveal that these fragments are copy-pasted fragments from textbooks.

What should I do in these cases? I feel that being too harsh might come of as being mean, but I would really like to emphasize that the practice is very bad for the scientific community.
As Mikael said, copying and pasting from a textbook (or any other source), unless it's properly quoted and cited, is plagiarism. Now, it's possible that this varies a bit between fields and between cultures, but generally speaking, plagiarism is one of the most serious academic offenses, probably a step below outright fabrication of results. Well-respected tenured professors at major universities have lost their jobs and had their careers destroyed by a single instance of plagiarism. The point is, this is a very big no-no and you should treat it accordingly. You should definitely notify the editor, and see how they would like you to deal with it. I don't know exactly how that process works, whether the editor will just handle the paper themselves and let you know that your review will no longer be necessary, or whether they'll ask you to finish your review anyway and state your objections in it.

In the latter case, I would write an unequivocal recommendation against publishing the paper because of the plagiarism. Personally, I would be inclined not to even look at the scientific content of any such paper, although that may not work out in practice. But anyway, just pointing out the plagiarized parts and recommending against publication, in and of itself, is not mean. Just don't get carried away and start attacking the author. You could apply the same principle that is used at Stack Exchange, namely that it's about the behavior, not the person.



If you put aside the plagiarism, there is also the issue of sloppy English that you mentioned. In my experience, (nearly?) all reputable journals require papers to use proper spelling and grammar for standard English, or something reasonably close to it. Usually, the instructions for authors will advise non-native speakers of English to get a native speaker to check the paper for grammatical errors before submission. So it's reasonable for you to point out any such errors that you come across. Now, grammatical errors don't have to condemn a paper to oblivion the way plagiarism might, but if the grammar is bad enough, I would think it reasonable to recommend against publication in its current state. If the underlying ideas are sound, and otherwise qualified for publication, then you could recommend that the authors edit the paper to improve the grammar and resubmit it.