Paradoxes depend on the same matter interacting. When Cole injects his younger self's blood it causes a paradox however the matter of the human body is replaced every 7 years, blood even more frequently. As such there would be no matter in common between the young and old Cole's blood.
At the 4.5 minute mark, Katarina gets into a cab in New York City, NY, United States that has a license plate that reads "3A83" and a roof light that reads "80N1", which should not happen. In New York city the license plate and the roof light numbers will always match unless someone has illegally changed one of them.