When Mohinder is at his father's apartment and HRG is on the other side, Mohinder picks up his glasses and puts them back down on the right-hand page of the book. In the close-up they are in the middle of the book.
A solar eclipse is not a global event, and its point in time and duration highly depend on the observer's position on the planet. It is impossible for an eclipse to happen at the same time in New York and Tokyo as depicted.
When HRG is in Mohinder's cab, there is a quick close up of his permit to drive the cab - the expiration date shown is "02/30/07". It is also misspelled "Vehicle Oprator's License"
Several characters are shown looking directly at the sun during a partial eclipse. In reality they would all suffer serious eye damage from doing so. Only Niki, who views the eclipse through a pinhole camera, uses a safe method.
Since Claire Bennet can regenerate from any injury, it seems that the holes for her pierced earrings should close up when she does not have any earrings in. This does not, however, seem to be the case.
While sitting in the karaoke bar, Hiro tells his friend that he got his understanding of how time works from X-Men number 143, where Kitty Pryde travels through time. "Days of Future Past", the referenced comic book, was actually X-Men number 141.