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Firstly, please upgrade your iOS to 6.1.3, which should fix a few errors for you, and upgrade your spotify (current version it 0.6.1.48).
Secondly, are these songs you are trying to play in offline mode (i.e. synced) or are you streaming over your 3G/4G/Wifi network? There are sometimes problems with streaming when the time it takes to stream the song isn't fast enough and the song stops to wait for the buffer to download some more of the song so it can play, and it repeats itself (that would explain why rewinding the song fixes it, as that part of the song is already downloaded). If you haven't already, try syncing your songs. If you need to stream them for some reason, if you have the music quality set to high or extreme, lower it to normal and see if that helps).