I just scanned my computer with Aluria's Spyware Eliminator and it found quite a few nasty entries in my registry. I only have the free version so I can't clean the problems, so I was wondering if it would be ok to just use regedit in safe mode and delete the entries. I assume the answer will be no, but I'd appreciate feedback.

Unless you are very sure of what you are doing, editing the registry can be hazardous. There are several good spyware programmes (both free and highly recommended here and elsewhere) that will allow registry changes to be made, but also creates a back up of the original, in case something untoward happens after the changes are made.
Ad-awareSE and Spybot Search and Destroy are both good applications, and are updated on a regular basis.
Cheers,
John