Around the 30 minute mark, just as the away team leave the tunnel into which they beamed, Tasha moves her phaser from her right hand to her left. When they round the next corner the phaser is back in her right hand.
As Tasha and Worf start their phasers to burn a hole in the cave wall, you can see the seam of where the wall will fall through, especially on the left, where Tasha is firing.
The images from Beverly's visual record of Jameson's de-aging were screen grabs from earlier in the episode, not images that Beverly could have taken in her duties as a medical officer.
When Picard enters the bridge from the turbolift with the camera following behind him, the picture jiggles a bit, as if the cameraman missteps.
Anne Jameson is putting clothes away in her quarters. The door opens and she starts talking to her husband before she sees that it is him.
Immediately after informing Capt. Picard of increasing speed to Warp 8 on the bridge, one can clearly see the prosthetic on Adm. Jameson's neck that make him appear aged is peeling off.
Before Jameson says he's going to lead the away team, Riker, Picard and Troi are all sitting in their usual chairs on the bridge (in that order). In the next scene, the seating order is Picard, Jameson, Riker and Troi, meaning that Will and Deanna both moved to other seats, just so Picard could sit in Riker's spot.
Anne refers to Karnas's recording as a "tape." Referring to recorded footage as such is a decidedly 20th century term. Even in the world of TNG they knew that magnetic tape would be a long-outmoded storage medium.
A great deal was made early on in the series about not allowing the captain of a ship to beam down as part of an away mission. Here, both Picard and Admiral Jameson beam down as part of an armed contingent to try to take the hostages by force and Riker registers no complaints.
Picard proves to Karnas that Jameson is who he says he is by showing him a series of three photos purporting to be of Jameson de-aging. Karnas is convinced, but doctoring up such images would be easy to accomplish in the 20th century, much less the 24th.
When the away team beams down to the planet, Jameson, Worf, and Tasha all carry type II phasers (the so-called "Dustbuster" style) while Picard, Geordi, and Data carry only the smaller, less powerful type I phaser. The entire away team should be equally armed, especially since they are going in expecting a fight.
When Picard leaves the bridge to go greet the admiral, he uncharacteristically contorts his face just before walking into the turbo lift as though stretching his jaw or speaking.