Thanks for replying, I hope Apple Support helped straighten things out. To clarify though, at the end of the day when attempting to shut down the computer for the night, the computer would be terribly slow in shutting down - like 5 minutes or so. Then it would restart itself without me asking it to, and a message would come up saying something like "you attempted to shut down your computer and there was a problem. Send a report to Apple?"
I called Apple Support after posting my question, and the technician had me restart in safe mode and that seemed to resolve the problem. I'm hoping it remains that way. Martin, Apple's technician, suggested that safe mode goes further into resolving issues than disk utility. I'm so pleased with the quality of service I get from Apple Support.
Anyway, its shutting down again without doing a restart so I'm happy. Thanks for responding to my inquiry.