Be wary. I think you have seen enough on this boat to realize she has issues. If you don't want a project boat, then she is not for you. A well maintained C310 is a gem, and, with persistence, you will find one.Looks like the sent out the mechanic and the issue with the engine was a loose nut. We are going to do another trial on Sunday!
I was lucky to find my 2003 C310 back in 2005. I bought her as a used boat, of course, but she was still brand new. The previous owner had used her once or twice, and the engine had 19 hours on it. I started her maintenance with a clean slate, and she now has 1700 hours on the engine, and over 7,000 miles of cruising under her keel. Her engine and tranny and all components are original, except the raw water pump and starter. Her sails are original, with a do over on the main sail at Sail Care.
Anyway, the right C310 for you is out there. If not a C310, then the other zero series Catalinas are good alternatives.