Problems with time travel in story telling? It never holds up to even elementary questioning, because it's physically impossible. Time doesn't actually exist. The observable phenomenon we have dubbed time is a side effect of the degree with which space has been curved by the mass of an object suspended in it, or gravity. Nothing more. That's what relativity really is, not how gravity modifies the setting of how time passes by each celestial object. Not some time-space fabric or energy storing the memory of the past and computing the possibilities of the future. The only thing that has ever, or will ever exist, anywhere in the universe, is the present.
Problems with these problems? I simply LOVE time travel in story telling. I mean it is so romantic, so adventurous, wonderous, mysterious. I can't leave it alone. I can't stop trying to make it work.
Most recently it's forced me to take a long hard look at the nature of the Time Stream in my FF tribute lore, as well as the involvement of time travel and temporal mechanics within that canon.