At some point, I started getting a message about 311 characters of unexpected output at every plugin activation. The number is always the same, and it happens for every plugin activation, including reactivating plugins that were temporarily deactivated.
The exact message:
The plugin generated 311 characters of unexpected output during activation. If you notice “headers already sent” messages, problems with syndication feeds or other issues, try deactivating or removing this plugin.
Is this likely to be a problem with a plugin that has extra whitespace in its files or something? I haven't yet gotten any problems with headers already having been sent. Possibly it's related to the weird 404 errors I get in wp-admin, but that problem was around long before this unexpected output issue.