Factual error: The solar eclipses in the show that affected the characters' powers were referred to several times as "global events". In the episode with the second eclipse it's shown to be visible in locations thousands of kilometers away from each other at the same time. This is simply impossible, since a solar eclipse occurs when the moon passes between the Earth and the sun, casting a moving shadow that can be only about 250 km in diameter (for a total eclipse). The partial eclipse can be viewed in a much wider region, but the eclipse in the show was a total one. It's not a global event, but a local one.
Factual error: When Hiro and Ando stand in front of a cinema in Berlin, Germany, you can see three movies posters in the background announcing a Buster Keaton festival. The left one shows his movie 'Cops' - but the German title 'Politzisten' is wrong - it should be 'Polizisten'.