When Picard steps off the table into Vash's room, the laces on his right sleeve are untied and hanging down. A few seconds later, they are tied in a bow knot.
At the climax of his fight with Sir Guy of Gisbourne, Picard/Robin Hood runs him through with a sword and begins to run up the stairs in search of Vash/Maid Marian. When the shot changes, Picard is back on the landing, watching Sir Guy's body, then begins running up the stairs again.
As Robin Hood is about to be beheaded, Friar Tuck attempts to create a distraction by throwing a device into a fire grate, but the object bounces a couple of times and falls out of the grate through a hole at the bottom.
When Q is talking to Picard in his quarters, the mirror in the background changes angles. At first, it appears to angle down, as we can see the character's feet. Later, it appears to be flat against the wall, as we can see Picard's head.
When Picard/Robin Hood is about to be beheaded, the headsman is too close to accurately hit the neck. At such close range, the headsman would be lucky to even hit his target (the neck of Picard/robin Hood) with the handle of his pole axe.
This is set in the 12th century, long before the 8-string mandolin was developed (17th century onward). Alan-a-Dale (La Forge) should have had a lute.
The guards wouldn't have been knocked out when Beverly and Deanna smash pottery against the guard's metal helmets.
There is no way that Picard could have seen the tablet with the map of the ruins when he did, because Vash is in-between the two.
When Beverly enters Picard's quarters for morning tea, Picard introduces Vash and pronounces her name as if it rhymes with mash, as opposed to the way he and the other characters usually pronounce it (rhyming with wash).