I can't believe this hasn't made it over from the general forums into the ideas section set?
As soon as you have more than a handful of playlists, you'll be organising them in folders. At the moment, the web player simply unravels the folders and puts all the playlists in an unstructured, and usually exceedingly long, list. This makes it extremely hard to find them again. Not to mention that once you have started using playlist folders, you will no longer be able to manage your playlists, or add new ones, unless you use the native client. In effect, this makes the web player a purely passive app in which you have to be very careful not to break anything about your playlist structure. Also, you have to plan in advance if you want to use the web player: you have to use the native app beforehand to re-order the playlists, so that you can actually find the ones you plan on listening to when using the web player later.
Either hardly anyone uses the web player, or most Spotify users don't really use playlists? Because for everybody who does both, this has to be close to the number one annoyance with Spotify at the moment.