Firefly, Light My Fire - S1-E1
Revealing mistake: Courage winces and reacts before the stereo-zapper is fired.
Revealing mistake: During Kendrix's morphing sequence you can see that the editor did a poor job photoshopping the Ranger helmet and you can still see the white edges of whatever photo they used. It should be tight to the Ranger's helmet and costume like the rest.
Revealing mistake: Angelica and the other children are about to crash through the door to attack Lyra and Will. As Lyra runs past a cabinet, a lamp sitting on top is knocked over and crashes to the floor. Dafne Keene, who plays Lyra, reached over and very obviously pushed the lamp to the floor.
Revealing mistake: During the final battle there is a dual between Julius Caesar and Gannicus. At one point Gannicus spins Ceasar around and he is shown to wear modern day underwear.
Revealing mistake: When everyone is supposed to be frozen, the neighbor girl standing behind the car can be seen moving her hand onto the car. This happens as Monica says "I'm not afraid of you, Wanda." (00:24:25)
Revealing mistake: Janet is holding a coke in her hand that she is supposed to be conjuring up but is already holding it.
Lightspeed - S5-E8
Revealing mistake: When the HIVE Five exit the museum and are intercepted by Kid Flash, Mammoth loses both his pants and the artifacts he has before KF whizzes past him. It's best seen in slow motion; at normal speed this mistake is hard to catch.
Revealing mistake: The ghosts often cast shadows.
Suggested correction: You can also hear their footsteps. But I'm not sure this is a mistake, just their own perception. Within the ghostly world they appear and act just like they would in life.
The ghosts are manifestations of energy, therefore they have no physical body to block light. Even if in the ghostly world, physics are physics and there should be no shadows.
Revealing mistake: During the opening theme, when the children are watching the magician, you can tell they were not actually filmed together. The magician scenes are filmed more professionally using a sharper tape or film image, whereas the children scenes look more like a standard fuzzier film-type such as on a projector (primarily used at that time).