This course is an excellent introduction to anyone who is interested in what quantum computing really is and has a slightly technical background. I took a course which covered the same material in person at Princeton a year earlier and there were some things I thought this course made much clearer (quantum FFT for example). If you take this course you will learn a lot about functional aspects of the nature of quantum systems and quantum mechanics in general, without having to get your hands too dirty with wave equations. You will get a sense of how quantum algorithms work and where the promise of their exponential speed ups stem from as well as understanding the most significant algorithms discovered so far. I thought that the homeworks and tests were actually very good tests of skill which were right on the border of challenging and possible so that with focus you really learned something.
There were two things that this course could do better but neither was a very big detractor. Vazirani assumed a certain background knowledge of math and certain conventions which I and a lot of others just didn't have -- nothing conceptually difficult, just facts which I didn't know. This could have easily been fixed with a 10 minute math review video at the start of the course but instead I had to dig around the forums and find out that the problems relied on you knowing some facts about a convention in complex fields or certain differential equations, etc. It wasn't a big set back, but it was annoying that I had to spend a few hours teaching myself when it could have been a ten minute video.
The other issue was that we never really talked very much about how quantum computers could actually be implemented. The whole course we just assumed that if it became possible for quantum circuits to be built that these are the properties and algorithms which could be run on them. I think I would have very much enjoyed a week of lectures on the most promising current approaches and more explanation of the problems which have prevented them from being a reality so far. At any rate, my rating reflects the material which was there not the material which could have been there and this course was excellent.