Your Spotify playlists should be consistant across all of your devices, meaning if you are logged into the same account on your BlackBerry and your PC then starring a track should also star it on the desktop application. Is this not what happens for you?
If not, make a note of anything you have recently changed on the BlackBerry application and then force it to resync your playlists by going to Menu > Settings > Reset Playlists. This will get the app to resync your playlists with the Spotify server, but any recent changes might be lost.
That is very strange, I just tested this on my Bold 9900 and the starred track appeared on the desktop client within seconds! Are you sure your phone is in online mode? Can you search and stream tracks?
Can you try the steps outlined by me in this post?
It will remove all of your playlist files manually and then force the client to redownload them again.
Can you just double check the tracks aren't being hidden on the desktop version by going to Edit > Preferences > Playback > (Untick) Hide unplayable tracks and then navigate back to starred, can you now see the tracks?
Okay, I have escalated this topic to the community team for you asking them to look into your playlists on Spotify's side (since I can't access that information). As its the weekend, they are normally light on staff but I will make sure someone looks into this for you as soon as possible ;)
Can't seem to find anything wrong with your playlists. It might just be some lag you are encountering. Below are the last 3 tracks I can see that you have starred. Did you do any of these on your Blackberry?