Farnsworth said that they fixed the time travel paradox when the crew finally stopped and killed their latter forms. However, they no longer exist in the first universe and the crew of the second universe presumably also travelled to the future. If this is still true, then the crew of the third universe should go forward, but do not. Then, the crew of the fifth universe (if such a universe exists) cannot be killed, creating another paradox in that they're meant to be killed by the crew of the third universe.
On a billion-year-old Earth where all life is extinct, it is extremely unlikely that there would be sufficient free oxygen in the atmosphere to breathe due to the Sun's expansion.
In the year 50,000,000, the breast size of one of the women changes between shots.
The ruins of the Planet Express in the year 10,000 appear to be the one of the normal Planet Express, despite Leela making it more productive and big. Although this could be because production went down when Leela read Fry's greeting card, causing her to neglect ownership of the company or they moved to a new location at some point after that.
The Professor said that a new universe is always identical to the old universe, but when Leela is sitting at a table at a reserved seat on Cavern on the Green, the waiter is serving meatloaf instead of telling the history of Cavern on the Green just like the old universe.
The Professor also makes changes in both succeeding universes; first, he kills Hitler, then in the next universe he misses Hitler and hits Eleanor Roosevelt by mistake. It is also worth noting that the time machine "stays" in its original location, so the Professor would be aiming and firing his weapon all the way to Germany to kill Hitler. (Since Mrs. Roosevelt was a world traveler, there is no telling where she might have been when she was hit, but it's unlikely she would have been in Nazi Germany.)