In "Keystone City" when the brick wall falls to reveal a glass door, a man can be seen through the door.
In the opening scene when Data is portraying a character from Shakespeare's play The Tempest, a small card can be seen attached to the back of the book he is carrying (likely containing his lines), but after increasing the amount of torchlight the card is no longer there.
During the The Tempest sequence, Picard says the light increase is satisfactory after Data orders the lights to increase, but before they actually respond.
Even though Starfleet and Geordi know about a "theta flux distortion" and that it can destroy starships, they haven't bothered to design sensors to detect it (Geordi says they "haven't designed sensors", not that the flux can't be detected).
Even though they know that the safety protocols are disengaged, no one wears any protective gear going into the holodeck.
Worf asks a hologram couple if they've finished their jigsaw puzzle, even though he can clearly see there are several big gaps in it. Doesn't he know how a jigsaw puzzle works?
Data: Complex systems can sometimes behave in ways that are entirely unpredictable. The human brain for example, might be described in terms of cellular functions and neurochemical interactions, but that description does not explain human consciousness, a capacity that far exceeds simple neural functions. Consciousness is an 'emergent' property.
La Forge: In other words, something that's more than the sum of its parts.