Frozen clouds and mile high tidal waves in a 3 foot deep ocean are the most obvious issues, since the relativistic physics are largely beyond most people's full grasp and were actually handled pretty well from my limited understanding and research following my viewing. Definitely a touching movie.
I must say that I find it interesting how many atheists enjoy the movie, when the movie itself makes such a case for love breaking barriers imposed by cold, precise, exacting physics. To me, if one can buy the hope of such a premise, one can buy the hope of a Being whose very purpose is based on love which, according to Interstellar, can surpass our knowledge of physics. I don't want to get into any religious debates over this, but it's just a bit of food for thought.