Right here goes....bit long winded but it will work!
1) Make a copy of the songs (your playlist) in a seperate folder on the desktop by simply copy/paste from itunes into a "New Folder"....Name it whatever you like...
2) On Spotify go to Preferences/Settings and scroll down to "ADD A SOURCE"
3) A window should open to ask you which file/folder you want to add to spotify. Choose the "New Folder" that contians all the songs from your playlist and click "Open"
4) The "New Folder" should be on the list of sources that Spotify is looking at. Untick every other source on the list - Don't worry, you're not deleting anything, simply covering it from view. Once we're done you can re-tick everything and it'll appear again
5) Still in spotify...Open a blank Playlist (Probably File then New Playlist?) and name it.
6) Still in Spotify....go to "Your Library" and then Local files. You should see all the Songs on there from your "New Folder". Select them all with Cmd-A (or for you dirty Windows people CTRL-A), go to your new playlist that you've just named and paste them into it! Done!
Remember to re-tick all the sources again once you're done!!!!
Your method seems to work indeed.. problems I encountered: (i)it goes extremely slow using the app on my imac, (ii)it would be so much easier if spotify would just import the existing itunes playlists and (iii)my playlist contained more than 1000 songs, when trying to use it as the basis of a 'radio', it didn't work.. I don't seem to find an easy way to create a radio which is a bit varied - all radios are one-dimensional, per artist or genre and I just like mixing..
The only issue with this is that as soon as I delete that folder, Spotify can no longer locate the songs. I don't want to have to store duplicates of all my music. Really wish they hadn't gotten rid of this feature.
With the latest version of the Spotify app the "Import Playlist..." item is gone. But there is help: Have a look at this tool: iTunes2Spotify: http://itunes2spotify.mrupp.ch
It worked great for me, you can import your iTunes playlists to spotify and there are quite some options for finetuning like comparing the durations if multiple tracks are found. If a track cannot be found, you're able to do a manual search, etc... And it's also possible to add just the missing tracks to existing playlists.