Time travelling is hard. And I'm not talking about physically or mathematically hard here (which it also very well is). I mean it's really hard to get right in fiction. The only place where it is possible, as far as we know.
There are so many problems present in all the works of fiction containing time travelling I don't even know where to start. Maybe from he types of time travel.
There are two main types of travelling through time. First, there is the classical time machine where travelling happens through some sort of pseudo-scientific construction directly. The other option is the long way through either suspension or moving at relativistic velocities, sometimes even both at the same time. Using the suspension is probably the easiest and gets it mostly right.
The problems are as well two-fold. There is the technobabble, which is easier to forgive. After all its science fiction. But still, it would be nice to have some sort of root in actual laws of physics. The problem is they are often way more bizarre that you could come up just making that thing up. But in that way also harder to explain.
But if I can forgive the freedom of omitting some fundamental laws of physics the other problem is usually the bigger one. Breaking causality and making logically impossible things, paradoxes everywhere. Things that wrap the reality to a whole new level, if not ripping holes in space-time.