Wow. Very hard interview(s). I am a new-grad for reference, not interviewing for a senior level position. I was interviewing for a position that was listed as mostly HTML, CSS, and some JS. The initial phone interview went fine, as did the first skype interview (technical interview). I will go into the coding questions in detail below for your benefit.
I signed an NDA so I cannot tell you the questions specifically but I can give you advice. They make you write fully working (and tested) code for non-trivial problems on the spot in under an hour with an interviewer breathing down your neck.
The first question involved file parsing and file system operations (reading/writing files, etc). It also involved recursion and a stack in addition to just nuts and bolts knowledge of your preferred language. I would definitely recommend using a high level language like Python or Ruby because you simply dont have time to set up anything OO. This question went well for me and I finished ahead of schedule.
Next was a question involving a lot of logic and required you to really think through the problem on paper and draw some stuff. It didn't require any special algorithms but required pretty good logic and thinking skills and a knowledge of modular arithmetic. You dont have time to try multiple approaches to the problem, so you have to do it right the first time. This one went pretty rough for me as I couldn't conceptualize the entire program and approach before I started coding and ended up hitting some road blocks. I finished right on time, but was pretty rushed. Again, python or ruby (and taking full advantage of the high level features of those languages) would be a great choice as anything else would simply take too long.
Next was something web based. Definitely know js/jquery like the back of your hand, and do some practice coding some simple web apps from scratch in HTML, CSS, and JS, in under an hour. What screwed me here was a particular feature of the DOM I was unfamiliar with. I had to do two google searches for syntax and to see what the return value of a function was (so I could use the result), which didn't seem to please the interviewer. I finished in time and it was 100% functional, but my solution was not the most elegant as I was pretty rushed in the last 10 minutes.
At this point they stopped the interview and told me it wasn't going to work out, but thanks for coming. It's worth noting that I successfully solved all their questions, in the allotted time, and they still stopped the interview half way and gave me the bad news. They weren't looking for you to just solve the problems, they were looking for you to have a good, elegant solution with as little help as possible in as little time as possible.
I was also surprised that a position that was advertised as a front end position had such classical programming questions for interview questions. The third question was more what I expected going in. I was also surprised that they required you to write tests for all your code. They were very concerned with edge-cases (even way beyond the "practical" application of the code you were writing) and testing. You would think in an interview where the time is so limited they would forgive those things and mostly test you on your general skills instead of your ability to make a truly fully functional and tested app.