Sporadic problem: diamond question marks and gallery shows full-size images

We have a problem which appears and disappears seemingly at random. Or rather, we have two problems which appear and disappear seemingly at random together – so there must be an underlying problem causing both.

Problem 1: For some images, our galleries show full-size images instead of thumbnails. This of course breaks the layout – the large images overlap each other. The images themselves are uploaded and generated just fine (all sizes of the images are there in the relevant uploads folder). but for some reason, for some of them, the html that WP is generating uses the full size image for the src instead of the thumb. It’s possible that there may be some link with exif data – many of the images which have this problem have exif – but I can’t be certain that this there’s a consistent correlation.

Problem 2: The diamond question marks which normally suggest a charset problem. But our charset is fine – UTF-8 – and certainly hasn’t changed.

These two problems initially appeared together, lasted a few hours, and then went away again spontaneously. That was a few weeks ago. But now they’re both back, and showing no signs of going away again.

I figure there must be some issue with the server, as I can’t imagine how else two apparently unrelated bugs could appear and disappear together, when we haven’t changed anything at all in WordPress. But our hosts say that nothing’s changed on the server either.

I’d really appreciate any suggestions anyone has, as the site owner’s understandably going spare. I’ve been googling my fingers off, but have found no solutions. There are a few people who have had similar problems with their galleries, but I’ve yet to find a thread anywhere where the problem was solved.

Many thanks in advance,
Artemisian