Star Trek: The Next Generation - Sandwich Eating Crew Member Reflected in Crystal
You'll need a recording of this episode to truly appreciate this slip-up, because its so brief, you'll need to rewind and see it again.
In one of the "Spock" episodes, Spock, Data, and a couple of other crew members are being held captive in a room. Data generates some sort of hologram that creates a fake wall, behind which the captives hide, allowing them to surprise and overcome their captors.
In this scene, there is a large crystalline piece of artwork in the middle of the room. If you watch closely during this scene, there is a moment where you can see the reflection of a non-cast member eating a large messy sandwich.
You have to watch closely, and focus on the crystal rather than the action in the scene. Its visible only for a very brief moment, but its worth it... hilarious