||Picard claims that he has inspected Rasmussen's credentials and that they seem to be in order. Huh? Does Rasmussen really have an "Official Federation Time Traveller" card, and how would Picard know it was genuine if he did?
The Enterprise crew use the computer to disable a phaser by remote control in this episode. What a fabulously useful function for the computer to have! One wonders why they didn't bother to use it in "Power Play", "The Hunted", "The Game", "Datalore", "First Contact"...
At the climax of the episode, Picard must face a tough decision - he might be able to save the planet, but only by risking the destruction of the Enterprise. Wouldn't this be a good time to separate the ship and evacuate the civilians on the saucer section?
At one point Riker asks when historians of the future started using time travel to investigate the past. Well it happened a century ago, Will! The Enterprise was doing it in "Assignment : Earth" Silly Riker should have known this.
Speaking of things Riker should have known, Rasmussen asks him what he thinks is the most important example of progress in the last 200 years. Riker responds "The warp coil. Before there was warp drive, human were confined to a single sector of the galaxy." But First Contact shows us that humans invented warp drive in 2063, three hundred and five years before this episode. And in First Contact, Riker and everyone else talks about that event as something that is extremely common knowledge - how could he possibly not know this date?