Well, the thing is, the problem does not always occur. Also, not always on the same blocks... This makes it very hard to investigate, of course.
It seems to me it has something to do with the block-renderer, when you have several (more than 5) custom MB blocks in a page. The more custom MB blocks there are in a page, the higher the chance that one or more blocks will have this error. Sometime when I reload other blocks have the issue, sometimes all the errors are gone.
I've seen this behaviour in multiple websites where I integrate custom blocks into a custom-made theme, using the MB Blocks extension of Meta Box.
Do you have any other ideas than the ones you proposed?