I managed to figure out how to fix this on my iphone 4.
I went through and deleted all of the songs with the grey dotted circle next to to the from the "on my iphone" list. you have to do that individually, by right clicking on them, clicking delete, and then hitting okay when it asks you if you want to delete them from your phone.
I then went back to my itunes library and made sure the songs were in all the playlists I have on my phone, and dragged them in if they weren't. (If you usually sync your whole library onto your phone it should be fine.)
Then I went back into the device and checked 'sync only checked songs and videos', then went and checked the playlist i wanted under the music tab (or just check 'entire music library' if thats what you want.)
Hit sync, and it should add all the grey dotted songs one by one, the circle sort of goes around like a timer.
If this doesn't work, i would try manually adding the song by dragging them from your library into the device when it appears on the side, after deleting them from the "on my iphone" list.
Hopefully this helps (: