Factual error: The rock samples are from "22 years ago this month," and the solar model predicts a solar eclipse every 22 years. But in order for the sample records to be kept, they must be marked relative to an interplanetary standard. For the orrery to have consistently accurate meaning, it must be set to local years - revolutions of the mystery planet around the sun. One timekeeping is used for records that must be transferrable to other planets and the other for daily use like time of day, but the two cannot be mixed. This makes much more sense than applying the standard cycle to local time - it would totally ignore local events like day, night, and eclipses, all of which are very important.
Character mistake: When Carolyn first addresses Imam, she quite obviously pronounces his name "ell-mom," as though the capital I in his title were a lower-case L. It should be pronounced "ee-mam". We distinctly hear Ali call out his name in this fashion after the ship crash lands on the planet.
Other mistake: When Fry is looking around for Riddick at the end, she's holding the blue bottle of bugs to light her way. The blue light on her face isn't from the bottle as she holds it, as she's circling around in some cases with the bottle completely behind her, yet her face is still lit up blue.