I do not think there would be an unique criteria, in my personal view, i tried about three before decide, for me the most important thing was patience and knowledge, also, to be comfortable with him/her.

I had experienced tutors that run so fast paced that it was almost impossible to follow and another who just was sooo difficult to immitate pronunciation and that is very important when learning a new language. In my very personal case i do not need to learn the new language for work or life, for me it is just a hobby ( a hobby that i take seriously, like going to the gym for some people), i just think it would be nice to speak a third language.

I settle up with a tutor who is patient, knows the language, know the slang of the language and also has a good pace for the course. Something that i really appreciate in a tutor is variety, like when we just stop using the text book for a while and do a practice dialog, or a game or a puzzle, stuff like that make learning fun.

hope that helps..

That has been one of the best introductory videos I've seen on this site! :)  Really clever work in adding the animations.

If I were looking for an informal tutor, I would just look for someone who seems easy to talk to and is approachable. Like a chat over coffee.  That'd be the most important thing to me.