Revealing mistake: When Picard is trying to squeeze through the rock archway, he looks like he's stuck, but a closer look reveals he has enough room above his back to squeeze through without any trouble.

Revealing mistake: As Worf climbs up the side of the 19th century ship, you can see that his pants legs are red in front. (The paint on the ship wasn't dry when they filmed it.). (00:21:50)

Revealing mistake: Roads are visible in the background during the climatic fight sequence on Veridia III, even though the planet is uninhabited. (01:40:35)
Revealing mistake: As the saucer separates, the starfield behind it can be seen through the saucer.
Revealing mistake: As Picard looks up at the path of the missile, he's looking toward the sun, but the sunlight is coming from behind him, as evidenced by his face being shaded, and the back of his head lit.
Answer: Vulcans do live that long (300+ years), but it is not Tuvok. For one, his ears and eyebrows are human, not Vulcan, for another, Voyager tells us he left Starfleet for over 40 years shortly after the Khitomer conference, which was before Enterprise-B entered service.
Grumpy Scot