Well, the teachers' videos are crucial, without them it would be very difficult to choose a tutor. All written presentations are more or less the same and don't permit you to assess the real qualities of a teacher. I mean pronunciation, which is the key factor for me, and whether a teacher is prepared professionally. Because it happened to me to watch really odd videos when a tutor who claimed to be a professional teacher with pretty high hourly rates, recorded his presentation video with unmade bed and piles of clothes behind him. Or a teacher who talked in a too relaxed, not composed manner evidently without any idea what to say while recording his video. I seriously doubt that they are able to be in time, to prepare a decent lesson, to be attentive to all details and mistakes while you are speaking during a lesson.

As for the other factors, I would rather prefer a teacher with one or two languages learned up to at least advanced level as it proves that he or she has not only experience in learning but in achieving some results as well. 

As for polyglots, I would not choose a teacher who claims to be a polyglot. Because learning of any foreign language takes an enormous amount of time, not mention learning of several languages. So, I have a question: what is their priority - to teach or to learn?

I like for the video to be partly in English and partly in my target language.  I prefer teachers who can explain things in my language (English) if needed, but I especially want to hear how fast they talk and how clearly they speak in my target language and what their accent sounds like.  I also do not like videos where teachers ramble or go into depth about something unrelated to the language.  For example, I recently saw a video where the teacher said she was going to give an elevator speech (which is supposed to be a very concise explanation of what one does) and then she spent the majority of the video explaining what an elevator speech was instead of describing her teaching methods. My impression was that that teacher would waste my time going in-depth on explaining things I would not be interested in instead of allowing me a lot of time to practice speaking.   If their non-verbal behavior comes off as appearing arrogant or cold, that turns me off as well.

With italki putting the video at the top, I think that the first impression is now the still shot of the video screen before the video starts.  My suspicion from what I have learned about marketing and first impressions is that it would behoove a lot of teachers to re-do their videos.  Right now the first impression is of many teachers not looking into the camera, not smiling, etc.  I like to think I would not allow this to influence me, but if I were an italki teacher I would want the first impression to at least have me looking pleasant. 

The teacher's introduction video is very important to me. I've taken some on-line classes, not yet on italki, and the teacher video was a key factor to choose among the teachers.

Some teachers' profiles didn't really attract me, but after I saw their videos it really changed my mind about them, and vice versa. 

~ Good discussion topic, thx

Murad