Strange frame rate issue just started happening

FCPX 10.2.2.

I have a bunch of clips that have suddenly started acting strange, even when just playing them from the event list. For example, in one clip that's 23.98fps, if I slowly arrow through frame by frame, in every group of 4 consecutive frames, one frame is dropped (as if it was deleted) and a different frame is duplicated. If I "Reveal in finder" and play the original version, it does not have this problem in QuickTime 7.

By the way, Motion 5 has the same issue. If I open the original source file in Motion, and arrow through the frames, it does the same thing (duplicate a frame and drop another frame).

This clip (in fact all my problem clips) were fine yesterday during the day. Then I opened up the project again in the evening, and this started happening. I haven't changed anything - not in the project, not on the computer.

Starting a new Library and importing the original files doesn't change anything - the problem still occurs.

I tried creating optimized media for one of the problem clips. When I drill into the FCPX library file by using "Show package contents", and open the optimized media file (in the Transcoded Media/High Quality Media folder), using QuickTime 7 player, this optimized file has the same issue. It's been transcoded this way - dropping one frame and duplicating another.

Let me say that again, and let it sink in: The optimized file, which in theory should be a frame-by-frame copy of the original, actually has different frames than the original file. I would have said that's impossible.

This doesn't happen with all of my clips. I have some projects with clips that have no issues. These clips came from different sources, so perhaps it's a problem that only occurs with certain types of encodings, but that's just a shot in the dark.

And again, everything was fine yesterday during the day. And nothing got changed that I know of - not in the projects, not on my computer. I even tried rebooting and repairing disk permissions, but that didn't help.

Does anyone have any ideas? This is so strange - I have no explanation whatsoever. It's so strange that I slept on it, thinking I was dreaming, and everything would be fine in the morning. Alas, not dreaming.