I recently passed the 10000 rep threshold.
Are there now things to be more careful of/pay attention to, e.g. because flags and votes have more impact?
I don't think much changes about the tools you previously had access to. You should vote, review, close/reopen, edit, comment, and flag the same as you did before. Your flags don't now carry more weight, for example. In the low-quality review queue your "recommend deletion" option might be replaced with a "delete" option; I'm not sure if that kicks in at 10k or 20k. (At 10k you can vote to delete some posts, but is the review queue sensitive to that?)
You can now vote to delete posts under some circumstances. One thing to know is that, unlike other votes, delete votes can't be retracted and don't time out. Please do vote to delete stuff that really doesn't belong, but if you think it can be improved so it's no longer delete-worthy, try to help make that happen instead. This is a different pattern from "downvote because bad, and if it's fixed retract or reverse the downvote", and that's unfortunate. Don't be afraid of voting, though; when we moderators see flags calling for something to be removed we really want to see community involvement instead of just mod-hammering it.
Thank you for helping to maintain the site.