If we really could time travel, what complications might we face?

whatever happened happens. you can't change the past.

It depends on what kind of time travel it is. If it's in a machine, maybe jumping into the time stream or whatever, scrambles your molecules a bit and mixes them a bit with those of the machine. Maybe there is a specific amount of time that it takes to get to the place you want to go to, but in the time stream, there is no oxygen and we suffocate. Maybe the time machine lands somewhere like the ocean or over a pit and it breaks (though I suppose they could teach the travelers how to fix it.) Maybe someone falls out and becomes lost forever. Maybe we try the limits of the machine a little to much and it takes us to the edge of the world, or limbo (because, knowing how curious mankind is in general, someone WILL try to see how far they can go. Like maybe they try to see the big bang.)

There are so many possibilities

Well to start off time travel is possible, however it is only possible to go forward in time. Traveling backward in time would cause what is called as a "paradox". To travel forward in time, a train would have to be built that could go in a straight line around the world without any interruptions t close to the speed of light. This would cause time inside the train to move extremely slowly so if the passengers only age a week, they actually travelled hundreds of years into the future. Outside the train however, time would move normally. The train really would be traveling for hundreds of years, but the passengers would only age a few weeks

I would say that nothing perceptible would happen to those not time traveling.
Time travelers would only be able to travel to alternate universe in order to avoid the grandfather paradox.

the main problem as with star trek beaming and stargate wormholes would be that only a copy of you would travel and arrive as it would be impossible for exactly the same molecules to transport across space or time after a while it would be a copy of a copy of a copy and who knows what could happen to a traveler then, but basically it is impossible

Well, time travel is capable and in doing so, the only complication that I can tell you is dealing with a society that don't think it is possible. If you time traveled think about the difference of mind set you would have when you return. Think about the fact that you will not be limited by the same thought process of the individuals you work with and go to school with and your family, what do you think will happen to them all if you came back and told them of the experiences you had with your adventure. They would think you to be a nut. That mind of the non-traveling person is limited to compared to someone who can time travel. Time travel only requires that you think beyond space and time. Then and only then will you be capable of time travel. You realize that time is an illusion. Just like in a movie theater, you only see the movie being played. The movie is actually done. It is on the role and all you have to do is access the roll and look into whatever time you so desire. It is when the mind can leave this physical realm and somehow attract atoms on an atomic level to recreate this physical body again. The body is only a tool for the mind. Do you want to know how I know this?

Sooner or later, "Time" takes its toll on E-V-E-R-Y-T-H-I-N-G.
"Relevancy" and" Adaptation" effect the outcome. Unfortunately, ONLY "Time" will tell , as it is NOT what we "can" do, but what we" will". Peace.