Right at the beginning of Drucker's speech about cloning, after Dr. Weir's speech, the audio starts before his mouth starts to move. In the very next shot of Drucker, the audio and video are correct again.
When Gibson is bringing the 'lower intestines' up to Nu Organ in the red-and-white cooler, he takes off the lid to get his gun. However, during the shot where a female employee walks past and Gibson pauses, you can see that the lid has been replaced without Gibson touching it. The lid is removed again in the next shot.
When Gibson enters Replacement Technologies with the 'lower intestines' cooler, the guard asks if he can view the contents. He tears off part of the tape when Gibson mentions the flesh-eating virus. In the next shot, the tape is still intact. When Gibson picks up the cooler, the tape is loose again, and Gibson reattaches it.
When Gibson wedges the chair under the door handle in the holding cell, the seat cushion is facing up. The same is the case in a later scene when Marshall tries to force the door open. After Gibson escapes through the screen, the cops break in, sending the chair flying. In this shot, the seat is positioned cushion down.
After Adam has broken the TV screen in the police station, he leaves the room behind the screen and shuts the door. When Marshall and the police officers come in a few seconds later, they look through the broken screen and the door is open. In the next shot, you see Adam running away from the door, and now it's closed again.
The memory recorder displays only visions, not thoughts. If it displayed thoughts, the villains would have known that the other Gibson was behind the clone in the helicopter/jet other than by the reflection in the glass. However, this doesn't necessarily mean the thoughts weren't recorded, only that they either chose not to display them or couldn't come up with a good way to display them.
Simpal Cindy's eyes close when Gibson tells her to sleep. When he picks her up and brings her to the house, there is a shot of her eyes opened, but it's possible that the eye servos don't lock closed in sleep mode. Sloppy design, but not a goof.
Given that a dog is supposed to eat, it would seem illogical to have the option to make a dog with softer teeth. Since they are selling the dogs to rich people, though, it seems likely they would make whatever people are willing to buy, and if that means the dogs need a special diet, then so be it.
Fingerprints cannot be cloned. They are something that changes with each individual due to individual stresses during development in the womb. For example, identical twins will each have their own unique fingerprints despite sharing the same DNA. While scars and birthmarks are shown to be replicated, each and every insignificant factor would randomize and alter any attempt to replicate the print making it different. That alone would identify a clone through the many finger scanners in the film.
When Adam lands his whisper craft on the roof of the building, a security guard comes out to stop him. Adam provides his clearance to be there by presenting him with the contract he signed earlier in the movie. When the guard looks at it, you can clearly see that none of the lines are filled out.
The goof items below may give away important plot points.
When Hank poses as Adam to fly Michael Drucker to the top of the mountain, Hank asks Drucker "Hey, you own the Road Runners, right?", gets out of the pilot seat and exits to the right. Drucker looks out the left window, and immediately outside of the window is a man wearing a bandanna pointing a gun, who then shoots Drucker. Later, Dr. Weir is showing Adam the last thing recorded in Drucker's memory. Hank asks Drucker "Hey, you own the Road Runners, right?". Drucker and Hank continue to talk, Drucker looks out the left window where is body guard is standing and waving to the guy wearing the bandanna standing in the distance. The guy in the bandanna then shoots the body guard, Hank, walks up to the window, and then shoots Drucker.
In the last few minutes of the movie, Adam gives his daughter, Clara, a cat. When Clara asks "Can we keep her?" the camera is behind her, you see the cat's front paws are placed on the side of Clara's left arm. The scene cuts to a camera in front of Clara, you see the cat's paw dangling/sticking out and are not touching Clara's arm. The scene cuts to a camera behind Clara where both of the cat's paws are again placed on her arm.
The day after the two Adams escape the fight on the helipad, the camera shows the front of the Double X Charter building. If you look closely at the window to the left of the door, the reflection of two people near the helicopters are visible in both the left and right panes of lower glass, and right before the camera cuts to the next scene, a camera operator's reflection across both of the lower panes of glass is visible.
When the guy wearing the bandana shoots Michael Drucker through the window of the helicopter, the glass would have either been broken or melted (seeing as they are shooting lasers, not bullets). This is not shown later in the movie, and none of the Double X Charter employees notice that one of their helicopters' windows has been damaged.
However, if the cloning company can spend millions of dollars to clone several people on short notice, and cover THAT up, then you can be pretty sure they can fly the helicopter back, spend some money to fix the window, and easily cover that up as well.
When the premature clone of Drucker wakes up, he screams like he has just been shot, yet the neurosync was taken several minutes after the outgoing Drucker was shot. However, it is quite possible the new clone was uploaded with the neurosync only up to the moment of shooting, in order to spare him the unpleasant memories of the last few minutes of intense pain.
Talia and Wiley both were re-cloned after they died. However, both of them remember when and how they died; as we've seen, though, the syncording can be made up to a few hours after death if the brain is intact.
When the guy wearing the bandanna shoots Michael Drucker through the window of the helicopter, he shot Drucker right in the head. Later in the movie, Dr. Weir is playing back Drucker's last recorded memory that was recorded from his brain, they played back everything up to the point where Drucker was shot. According to the movie, this would not be possible since syncording can be made up to a few hours after death ONLY if the brain is intact.
When both Adams are at XX Charter building bombs, both have the exact same shaving cut on their left jawline from the previous day. This was initially used to distinguish which one of them was a clone in an earlier part of the movie.
This was actually a plot device to make the viewer think this was the original Adam. When the clone is captured by Drucker, it is explained that adding the cut and faking an old injury scar are easy to do.