Paradoxes occur when something is self contradicting. These are usually relatively harmless. The ones you need to be worried about are time paradoxes. If you were to go to the past and kill your grandfather before he met your grandmother, would you still be born and have been able to kill your grandfather?
Some other issues relating to time has to do with pulling something from the future to the past and using that information to create a future where that information doesn't exist.
These simple actions often cause the timelines to destabilize and eventually collapse.
Some people are really too reckless nowadays.