After 2 days having the same issue on my Lumia 720 with Amber update suddenly i had an idea that worked very well and I hope it can help others.
If you want to have your playlists first follow these steps
1) Using Windows Media Player create an empty playlist with the name you need/want.
2) Repeat the step one for every playlist you want to add.
3) Sync using the Windows Phone desktop app, remember this will only sync empty playlist that we gonna need later.
General steps (with or without playlists)
1) Connect your phone and be sure you can see hidden files, then delete all the content from the /Music/albums and /Music/artists folders.
2) Connect your SD card into a card reader and copy-paste your songs in the music folder, it doesn't matter if they have subfolders.
3) Put the SD card back to your phone.
If you are not using playlists, the above steps were all you needed... but if you are
1) Open your phone (not the SD card) and find the /Music/Playlists folder.
2) You will see every playlists you created at the beginning, open the one where you wanna add songs and notice that there's an empty list.
3) Having the SD card in your phone, open the route where the music you want in your playlists is (you may want to open a new file explorer windows).
4) Select all your songs and drag them into the opened playlist in the step 2.
5) Press Accept when it finish and repeat for every playlists.
Well that's all... I know it sounds like a long list of steps but it becomes very fast and easy but also I know this is not a proper solution and I hope MS could fix this once it for all.