WordPress 126.96.36.199 stable is out. I think this release was prompted by the trackback/pingback bug I mentioned earlier. It does indeed seem to be fixed now. After I deactivated the BlogTimes plugin, I could send trackbacks no problem. Here’s what’s said on the WP dev blog about the update:
Update: In our effort to optimize we made two mistakes in 1.5.1, one related to feeds and one related to trackbacks and pingbacks. We’ve updated the download with 188.8.131.52 which corrects these bugs and a few others.
So I guess I don’t really know if my problem was related to that bug or not. I’m just glad I can send trackbacks again. It was announced in the same post as the 1.5.1 announcement on the WP development blog.