The Federation flag has the Roman numeral MMCLXI, which is 2161, the year that the United Federation of Planets was founded. It's motto, "Ex astra, scientia" is latin for "from the stars, knowledge." See more...
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Star Trek: The Next Generation (1987) - 124 mistakes in entire show
Continuity: The creators re-did the titles from the third season on, but only from before the shot of the ringed planet, and they didn't make sure they matched. Compare the movement of the stars inside the rings and the star field outside the rings - they move in different directions compared to each other.
Continuity: Commander Data tells Picard the Saucer Section will arrive in 51 minutes. Riker's synopsis audio can be heard in the background without interruption, and shortly after Data says this, the cameras turn back to Riker and the Video synopsis ends. Riker immediately reports to Picard who then receives the message that the Saucer Section is in orbit. Now, Riker was watching highlights of video footage from the Bridge, of which we see almost all of it because there really wouldn't be that much to view. And that's really all he could watch since we don't have cameras in the "Q-verse" and we see the footage ending with the Q sphere chasing the ship. Also, the entire ordeal was far less than an hour so there's no way a highlight real could take an hour, not to mention the uninterrupted audio. We seem to be missing almost an entire hour.