Does there exist any way to see the most downvoted questions in this day/week/month/year/of all time on here? I tried doing a search for "most downvoted" and found this, which suggests the "dual" exists.
Stack Exchange Data Explorer handles a lot of such queries.
There is a particular post for "Posts with most upvotes, downvotes, total votes, highest and lowest total score". I don't use the data explorer enough to know how, but I'm fairly sure you can place time limits on the queries.
You can sort the "questions" page by votes and go to the last page:
This only works for "all time" though.