Jenny100 has already mentioned a couple of my pet peeves. I worked like a dog to figure out the mandela or snake puzzle in Beyond Time, and then discovered that I had one of the "right" solutions that wouldn't work!
And I hate any slider, but that one in Timelapse, where you had about a 25% chance of getting a conformation that couldn't be solved was the worst.
Not to mention the puzzle where you had to move the white squares at the end of Reah--even with a printed solution in front of me, it took about ten tries; there were so many steps that I kept losing my place.
Judging by the number of saved game requests we get on Hints, I would add the laser/robot puzzle in Still Life to that list too...