1) The schedule works for me: not to be underestimated! I almost never schedule my own language classes very late at night or in the morning. 

2) Looks friendly and doesn't take himself/herself too seriously, and natural - simple clothing, no excessive accessories or cosmetics, nothing that seems "fake".

3)  Video doesn't just sound like a copy of every other intro: I usually don't like it if a teacher repeats exactly the same script in different languages, and I also dislike the cliche that "I've studied languages too so I know which problems you're facing and how everything is sooooo hard". I like teachers who show enthusiasm in their intro and who talk about the process positively.

4) Moderate number of students and lessons: I used to look for teachers who has been around for a while and had taught many lessons because I took it as a sign of reliability. However, my experience has  been that teachers who have a well-established set of students already and have had many many lessons tend to be less willing to take on new students or make an effort to keep them. Just my experience.

5) Something new I have been trying: I have been contacting teachers with an initial message of inquiry before booking a lesson. The purpose is to see how fast they reply and what their attitude seems like. Some don't even bother to reply to a polite and brief inquiry, so I don't bother booking a lesson - it saves me money because it gives me a good idea what your interactions will be like. If someone replies quickly and in a personalized way, I book.

@Guyomar:

The number 4) - I totally agree with you. I've had the same experience. I also think that busy teachers with too many students can't be prepared appropriately for their lessons. I usually avoid taking lessons from them. I don't want to be "just another student". I don't like when a teacher at the beginning of our lesson looks or sounds like a busy person or even more when they are talking about their busy day. Then I feel like somebody who bothers them.

Also I avoid taking lessons from newly coming teachers/tutors, they mostly either will raise their prices or will leave italki or will change/reduce their timetable/availability.