Although oversize media could cause this problem, I've never seen that happen myself. But I HAVE had a "Media process error" happen spontaneously on a few occasions, and it was caused by an internal error at Ancestry's end when FTM tried to retrieve an image during the sync. I usually first spot it when the "Syncing media items" progress bar appear intermittently, even while I'm not syncing. Checking the Tree plan page shows the "Media: 1 not complete - process error" link and associated Process Error popup you describe.
I outlined how to identify the media item(s) causing the problem in this discussion: https://www.ancestry.co.uk/boards/topics.software.famtreemak...
Essentially, you go to the %TEMP%\FTM directory on your PC, drill down to the latest xxxxSyncMediaLog file and open it (using the password NGDuck). It's an XML file so rather cryptic if you're not familiar with that, but you should be able to identify the name of the file causing the error. Having said that, I'm not sure you can usefully do anything to fix it other than wait - in my experience it always resolves itself after a few days, presumably when Ancestry fix the problem at their end.
Coincidentally I've just got one of these now myself, as you can see in the attached logfile view. The missing media item this time is an Ancestry source image from Pallot's Marriage Index - it's nothing to do with a large file and isn't a newly added item, but for some reason Ancestry's servers just can't find it at the moment, hence the error. I'm just going to wait, and sooner or later it will hopefully fix itself.