I purchased a used (previously two owners) Nissan Note 10 days ago. It is now showing odd problems. The battery saving 'lights off function' suddenly failing and lights full on. The air con switch is also coming on.

I'm a single parent, not on high wage and did not take out financing, just bought within the budget I had when my old Note was written off last month. So

I'm very concerned about possibly having purchased a car with inherent problems.
When I got it home and went to put my 'old' rubber mats in I noticed that the floor was very damp. Current flooding problems obviously aroused concern and I discussed it with the dealer, who assured me that it was just 'damp' from carpet cleaning. However, I’m not so sure this is correct, what should I do?