Time travel has been so overdone in animation. But really now, what writer hasn't fantasized about a character being able to tell his younger self that something is a bad idea, or go back in time to meet a character who is dead in their own time, or see their parents when they were their age. The potential for comedy and/or heartwarming moments is almost irresistible.
But time travel always has it's set of risks. The potential for risk changes with author interpretation, and I think that stems from the author's personal tolerance for serious brain cramps. If you change something in the past it will effect the future, this is agreed upon; question is, have the results manifested already or haven't they? Will you return to find that what you thought you were trying to change was directly caused by your meddling in the first place (ex: the scenario in Artemis Fowl: The Time Paradox), or will you return to find Nazi Germany busting down your door? (incredibly unlikely, but this does seem to be a trope)
Though it's sometimes fun to speculate about the time stream, I think a major source of glitches would come from the time-travel hardware itself. My own time-traveling character uses a wrist mounted device called the Crono-Drive Series 3. It is a pretty standard concept of a time machine, able to jump back and forth over several centuries and little more than that, but it has a few issues. Longer jumps through time are inaccurate, with as much as a two year margin of error. Shorter jumps are better on the accuracy, but the corrections drain the battery. The battery takes about ten hours of recharge time (a process needing no electric cords thank goodness).
The character's father has the newest model, series 5, which is able to speed up or slow down time for the user. Useful in combat if you're likely to run into that kind of thing, but it too is a battery drainer. My character counts himself lucky with the Series 3 though. The Series 1 was a backpack with a 50 year jump range, and the Series 2... Well... let's hope you aren't very attached to that hamster shirt...
