Continuity mistake: In the scene where Jessica is in the shower crying and the power goes out, she gets out, puts on a white t-shirt and goes walking around the house. When she walks through the garage door and grabs a hammer, there is blood on the front of the t-shirt (right at or a little lower than her waist and looks like someone grabbed the shirt with a bloody hand). Where did it come from? She didn't run into anything or anyone. [There's a deleted scene showing her step on a piece of glass. She gets blood on her hands when she pulls the glass out, then presumably wipes her hands on her shirt. Still a mistake, as removing that scene means the blood appears from nowhere, but there's the reason.]
Continuity mistake: In the scene where Beldar has finished giving Gladys a driving lesson and they are sitting in the car, you can see that he has nothing on his lips. After Gladys kisses Beldar, you can see red lipstick. As the shots go from Beldar to Gladys and back, you can see the lipstick disappear and re-appear.
Continuity mistake: In the scene where Gard telepathically fights an alien, you see his nose bleeding. Then the alien explodes, and in the next shot of Gard's face, the blood under his nose has vanished, only to return in the next shot of his face.