I have not read the books. What are the other racist tropes? Levelled at JKR? Besides the Irish guy blowing stuff up with a very Irish name?
None as obvious as the goblins / Jews, because, on the whole, the story is about white people. Different races come across mostly as tokenism, and on the whole there is very little charcterisation at all.
But even within what there is there are stereotypes: the token black wizard being called Kingsley Shacklebolt and helping the white saviours. Cho Chang (two surnames that certainly sound East Asian, but fit no real naming convention, and presumably the name is simply to accentuate the fact that, gasp, she's from E.Asian descent) mostly being used as a love-interest. And yeah, Seamus Finnigan, blowing things up, and of course, the one character that tries to turn water into alcohol is Seamus - playing into the "drunken Irish" stereotype.
Stereotypes are a common tool in Western culture (I have next-to-zero experience of any other). They're easy, familiar, and efficient. Most of the time they just drift us by, either because they're genuinely harmless, or because of our own blindspots, and often we might recognise them as "being a tad off" but not sufficient for us to do anything about it. There are times, though, when their use, unintentional or otherwise, sticks out and makes us go "um, excuse me?" In HP books
There are other somewhat "off" ideas, such as House-Elf narrative that promotes the idea that enslaved people are better off, or even happy, being enslaved. Sure, Hermione tries to stand up for house-elf rights, but it's for comic relief rather than treated with any seriousness. Dobby's the exception in elf-world, in that he actually
wants freedom. More evidence of lazy writing than anything else, I think (i.e. have a point to make for plot purposes, but fail to go any deeper into the underlying issues raised, and thereby risk perpetuating negativity: "slaves like being slaves!")