(at around 21 mins) When Arkin first breaks into the house, he uses lock pick tools. The straight flat one he inserts in the bottom and the jagged one on top. However the jagged edges are pointing downward and would not be able to click the tumblers.
(at around 1h 5 mins) After the girl and the hero electrocute the old man. The collector grabs the old mans feet to move him. The water that previously covered the floor is gone. The wood floor is dry.
Arkin is wearing black sneakers when he enters the house, then as he's walking through, he comes across a trip wire and it shows the boot of the Collector. Then when Arkin is walking down the stairs into the basement he is wearing some worn brown boots - a total of three different pairs of shoes within 5 minutes.
When Arkin tries to release Larry from the box we see that his feet have been pinned and he is chained. When "The Collector" picks Larry up after the electrocution we can see that Larry's feet are clean with no wound marks.
When Arkin and Hannah retreat to the room with the fish tank, the door is hinged to swing inward. The door the killer bangs on is hinged to swing out towards the hallway. When the door breaks open, it swings inward again.
(at around 57 mins) When the daughter and boyfriend are making out in the kitchen. He tears her shirt off of her. When she jumps up after seeing the collector she pulls her gray sweater over her chest. In the next scene her white shirt is buttoned up again.
The goof items below may give away important plot points.
In the opening scene, crickets are seen inside the lamp of the light post.Crickets do not fly, nor climb very well, so they wouldn't be inside the lamp.
Also, the roaches in the jar in a later scene are Madagascar hissing roaches. They are completely harmless, herbivorous and wouldn't have tried to or been able to bite or burrow into flesh.
(at around 1h 12 mins) When the policeman looks into the window and sees the dead boyfriend's body, the camera moves over the body and it can be seen that one finger slightly twitches. While the viewer might assume this was unintentional, it may have been on purpose to establish that the boyfriend continued to live, albeit in a horrific fashion.