I too have had precisely the same problem with my Apple TV gen 1. Its happened to me on both Argo (rented around 2 March) and Taken 2 (rented around mid-February) but I haven't experienced it previously.
Both times, I have written to Apple customer care and they have refunded the movie which is appreciated.
However the fact that it has happened to both of us (I am using the UK iTunes store) and has happened on different movies, does make it seem to be more than what might otherwise have been written off as an isolated incident.
My one concern is that perhaps Apple have started encoding the captions in a new way which may be supported by newer devices but isn't compatible with the 1st Generation Apple TV. <<< This is only a thought I've had and I'm happy to be told otherwise.
Does anyone else have any insight into this?
Actually I have just some further digging and come across this thread https://discussions.apple.com/thread/4400114 it seems to be a bigger problem - but unfortunately not one which Apple has acknowledged