Just because a trainer doesn't have those certifications or a degree doesn't mean they aren't any good. Having all that does mean it's more likely they have the necessary knowledge, though.
I would ask the trainer about what kind of certifications he has, his experience, etc. Some larger gyms have more requirements for their trainers than the small local place that may hire anyone off the street.
Word of mouth is very good, too. See if you can find other people he has trained and ask them about the trainer.
I'll admit that my wife is a personal trainer. She doesn't have a degree, and her certification is through ISSA. For the types of clients she prefers, her knowledge is adequate. She works for a large gym with lots of other resources for her to go to for advice. Her clients seem to like her because they keep coming back.
Yes, there are some wackos in the business.