Take a look at the two images below. The first comes from the first 10 seconds of a YouTube HD video in full screen mode. The second come from the same video about 20 seconds in.
I think the poor resolution is by design. YouTube has configured the video to start almost immediately after the user clicks play, but to do so, it must start the video with poor resolution in order give the high resolution video that's being cached on the client machine a chance to "get ahead" of the playback. Once the there is an adequate quantity of high resolution video in the video cache on the client machine, the player automatically kicks over to the high-res video. (If the user's broadband connection is slow, it may never kick over.)
Is my synopsis accurate? And, if the user really wants to see the high resolution from the outset of the video, how does she do so?