On the planet, when Riker puts the glass of lemonade down on the table, it contains more than in the previous shot when he drank from it.
On Q's planet, Data only has one pip on his collar in several shots.
During numerous shots on Q's planet, Datas rank pips which are usually from left to right, one hollow, two solid have been replaced with one hollow, one solid, one hollow, not only is this not his correct rank but no such rank exists in star trek lore.
At the end, on the Bridge, Q berates the Captain for his 'jealousy'. The correct term is envy, not jealousy.
All of the supposed French uniforms and scene dressings identified by Data as 1790-1800 are incorrect. The "Marshal of France" uniform in red is an unknown variant, as French forces did not dress in red. Correct colours would have been blue, green or white. The bell-top shako worn by the infantry was not adopted until 1804-5. These troops should be wearing a bicorne to fit in with Data's statement.
When Q, Tasha and Picard are on the bridge and Q says 'Penalty over,' someone can be seen right behind Q for a couple seconds.
That's Picard. He then walks around the console to face Q.
That's Picard. He then walks around the console to face Q.
When Worf runs to attack the Napoleonic creatures, one of them swings the butt of the musket at him, clearly missing him, but still knocks him down.
The beast-soldiers' "cannon" is a simple tube on a carriage.
When Data is clearing away rocks to rescue a trapped colonist, the rocks can be seen flexing and bouncing slightly in ways that an actual rock would not, revealing them to be made of a softer, lighter material.
When Riker is addressing the crew on the bridge of the Enterprise, you can see a fly buzzing around him.
The soldier-creature playing the bugle clearly isn't playing it at all, rather holding it to his lips.
After Q is forcibly recalled to the continuum, among the alterations to the bridge, which include the disappearance of the Klingon female and Wesley being reverted to his proper age, several characters are inexplicably re-positioned. Data and Geordi are seated at the ops and conn consoles, while Riker moves to the first officer's chair, and Beverly and Wesley are moved near to the forward turbolift. All of those characters had arrived at their previous locations on the bridge under their own power, so they should not have been moved by the undoing of Q's actions. If they were meant to have been reverted to their locations prior to Q's interference, then Beverly and Wesley should not have been on the bridge at all.
Q declares Tasha's penalty to be over, yet she is never returned to the game, rendering his statement meaningless.
When Q appears on the bridge, Worf and Tasha start to rush toward him with their phasers drawn. They should know from their previous encounter with him at Farpoint that phasers would not have any effect on him.
After she is given the order to raise the shields, Yar says, "Shields and deflectors up." The Deflectors would already be up, as they are used to keep particulate matter from striking the ship at warp (faster than light) speed. The shields are the much more powerful force fields used to protect the ship from attack.
The banner used by Q in his pavilion on the planet is "azure, three fleurs-de-lis argent." His attire and the period involved is described as "18th or early 19th century." The banner, as shown, was designed in 1902 (20th century), for inclusion in a stained-glass window of the cantonal Court of Mulhouse. The arms recall both Saint Louis, the patron saint of the town, and King Louis XIV, the founder of the town.