After spending two months with rdio, I still love it enough to stay subscribed (though I don't know if I am getting enough value from the mobile player!) I love the ability to listen to whatever I want instantly. Although they don't have a perfect selection (no Pixies, Arcade Fire, Spoon, etc), the selection is very good and getting better. And I have spent many happy hours discovering and listening to music that I probably wouldn't have discovered if I didn't ave access to the service (for example I am sure I wouldn't have spent two days tolling the Trojan catalog and rediscovering 60s Ska, and Rocksteady) and building playlists. The choice of licensing all the AllMusic data was an excellent one, and However, there are a ton of small annoying aspects of Rdio, which hopefully will be remedied shortly!

1. Maybe due to the fact that I live in Canada and the Canadian and American catalogs are very different there are a ton of unavailable albums, which Rdio insists on showing.
   There should be an option to turn off unavailable songs, especially on the Recommendations page (which is particularly frustrating when half of the recommended albums are unavailable). At least the unavailable tracks should be shown last, as frequently (at least in Canada) you will see that an album is unavailable only to see a different copy of the album available on the second or third page.
2. Genre is not an available way to search music, since this data is clearly available in the AllMusic it should be integrated into the service (the more that rdio makes music discoverable the better). Especially in the Top Charts, which for me is a completely pointless endevour without genre.
3. While playing on the desktop the music sometimes cuts out (or more often at the end of a track the next track is not played). I am sure that this is something that they are working on, but it is annoying to say the least.
4. The collections feature seems almost useless, it makes things a little easier to find in the mobile app (slightly faster than searching) but in the desktop client the Collection takes so long to load it is almost always faster just to search. More should be done with the collection in being able to improve recommendations and the like, but for now it seems like a big waste of time to your Match Your Collection. Adding artists to your collection also seems like you are just adding things to the void, and what you really should do is add to a playlist to check out later (which I currently do). Maybe if I paired my collection down, it would be better but for now it is a frustrating feature.
5. The Desktop Air Client seems only to be another annoyance. It is the only way to Match your collection (however, as I have stated above that seems to serve little purpose), but beyond that it serves no purpose other than something that seems to want to update the Air Runtime and update itself every time I start (with no apparent features added). It isn't even smart enough to stay logged in, and you must have a browser window with RDIO open when it starts up or it won't be logged in. I really fail to see the purpose the application, since you really need to have a browser window open to use RDIO anyway, and the Desktop Application seems to add nothing to the experience.
6. Recommendations (and almost all notices) are sent via email (which tend to end up in Spam filters no matter how often I mark them as not spam), which seems a contrary way to develop a social network, adding a simple messaging center to the interface would be simple and make a lot of sense. Or at least on your Recommendations page have the recommendations that your friends have made for you available (since the recommendations engine is so weak already).
7. The recommendation engine is clearly just mining the Similar Artists data from AllMusic, but at least check to see if that artist is already in my collection, and as stated before is available. I expect that the recommendation engine will improve over time as Rdio will be able to mine its own data!
8. The ability to create Radio Stations based on artists is nice (and is getting better with last update giving a little more control), however the ability to create Radio stations based on multiple artists (ala Last FM and Pandora) seems an obvious addition

There are a ton of other little things (Heavy Rotation isn't actually heavy rotation but the last few albums you have played), you should be able to click a single button to add all the top songs from an artist to your queue, etc but for now those are some of the big (and mostly easy to fix) complaints I have about Rdio. As it stands, it is by far the best way to listen to music on a computer and/or phone device, but this is a market that is going to start getting crowded (Google, Spotify and Apple will probably be entering in the new year) and if they don't quickly work on improving they will find themselves on the outside looking in as people flock to better services.