Well, me and my big mouth. Turns out there actually is a default setting to prevent spam of various functions. Edits are limited to 8 per minute. I've upped it to 30 a minute for now, while there's cleaning to be done that requires lots of small changes, like you said.
But the problem of some pages being uneditable remains. I just found one such page in the sysop area, it's the first and only one I found. I might have to ask my host to work some voodoo.
I managed to find a simple way to fix pages with the category bug. Simply edit the page. Just adding a comma or something is enough. After the page is saved, the category will be corrected.
And in the course of investigating the previous bug I noticed another one: people in completely wrong categories. Eron Gjoni was listed as a video game journalist (but not as journalist) despite the article being tagged as people. Fortunately, this bug is solved the same way as the previous one. Just editing the page will put it back in the category(ies) it belongs.
I think these sorts of bugs must spring up when importing databases and such.