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.).
Other mistake: If you watch the holodeck doors as Picard leaves the holodeck after hearing the bad news, you can see that the holodeck doors seem to be crudely painted with a brush and you can see the large brush marks.
Revealing mistake: Roads are visible in the background during the climatic fight sequence on Veridia III, even though the planet is uninhabited.