That is worrying. This thing is full of components on multiple PCBs and trying to replace them all would be quite the task.

I opened up the metal TBC C.B.A box mounted on the bottom of the VCR (see attached pictures), and while I'm far from an expert, I couldn't see any bulging caps or sense any strange smells. I'll have to look into it a bit more when I have the time.

In my case it wasn't bulging or anything, but it tested clearly bad on my ESR meter. It's possible you could locate which one(s) it is with cooling spray as well. I think it was C9518 that went bad in my case, but I don't have it with me right now to check. It might be a different one in your case though. The ones involved in power filtering (ones connected between power and ground) are the ones that take the most stress and are more likely to have issues (electrolytic ones, black can-shaped. The small brown ceramic ones and the yellow film ones rarely cause issues). The board is double sided with solder on both sides, so actually desoldering the cap was a bit of a pain.