When I installed VB6 on Win7-64 (using instructions easily found by a search engine), it worked fine. UAC was off -- i.e. set to "never notify."
After a few weeks I turned UAC on -- i.e. set it to its default. VB6 then couldn't compile because of the "Error accessing the system registry" problem. Unfortunately, turning it off again didn't help. Apparently the damage done by turning it on was irreversible. I can't explain why this should be, but that's my experience.
Giving REGTLIB.EXE administrative privileges while leaving UAC off sounded like a great idea, but that didn't work for me either.
Finally, using Process Monitor and PsTools as described in other posts here worked. However, I had to give Full Control to large parts of my registry to Everyone. This didn't apply just to isolated keys. It seems that the compiler needs to add keys to major nodes, so I had to open up these entire nodes.
Aside from the fact that working through these steps took hours, I'm now much more exposed than I was before I tried to increase security via UAC, However, I need VB6 and don't see another solution short of a new computer.
Lesson: Don't use UAC with VB6. Except if you've arrived here it's too late for that.