Plot hole: In the scene where Ashley Judd runs away from her attacker and falls into her aquarium he has moved to the bottom of the stairs - there is no way he would have been able to move that full fish tank. It looked to be about a 30 gallon tank - it would weigh about 400 pounds with the stand and even if he slid it with some superhuman strength, glass tanks are notorious for shattering when you move them full. Plus it would've made enough noise to wake the dead - no way she wouldn't have heard it.
Plot hole: When Nick confronts the P.I. and yells "Why are you following me?", he looks inside the car and see the file with his picture on the front seat. The P.I. notices this and turns the file over. After Nick grabs his gun, the P.I. jumps out on the other side, raises his hands in the air and tells him someone hired him and runs off. As the P.I. runs off, Nick yells "Who hired you?" as he stands alone next to the car. He then waits a minute and walks off. If he really wanted to know more information, he could have taken the file that was right in front of him on the carseat. It makes no sense that he is desperate for information about the strange events that are going on, sees this file on him, and yet doesn't even pick it up or look at it. (00:59:55)
Plot hole: Barry gets killed violently at the pageant. So obviously there should be blood everywhere. When the police go up to the crime scene, they find nothing. There's no way the killer had time to clean up anything, let alone drag away Barry's body without someone seeing him. And blood starts dripping after the police leave the scene.
Plot hole: Kazam is supposed to be a math genius, something that the plot hinges on, but he makes several mistakes when calculating the number of prime factors to find out whether a room is trapped or not. He says that 462 has three prime factors, when it has four, that 206 has four when it only has two and that 563 has two and 911 has three when both are actually prime numbers.
Plot hole: During the Congressional hearing, it is suggested that the alien signal could have been faked from a satellite - as Ellie only has her own experience to go on, it leaves her believing what happened, but still with an element of doubt. However, as a professional astronomer, Ellie would have immediately dismissed this since a simple parallax (triangulation) would have confirmed that source was at the distance of Vega - a distance far too great for any rocket to reach. (This is mentioned in the book). In fact, this is mentioned early in the film, when the employees in New Mexico calculate the source of the signal while it is transmitting prime numbers.
Plot hole: It is highly unlikely that the murderer knew Phil was going to put his ear to the stall when he heard the babbling. It is even more unlikely that the murderer is going to get him on the first stab through the stall. (Which also requires a lot of strength). We also have to assume that he spent time hanging out in the bathroom knowing Phil would go there to begin with, and that other two men with weak bladders were doing the same simultaneously forcing the victim to go to the stall to begin with. (00:07:45)
Suggested correction: The killer is incoherently whispering in a strange way in the adjacent stall to lure Phil to press his ear up against it. After stabbing him through it, the killer inspects the knife inquisitively, as if checking to see if he actually got him. While it's still not a terribly plausible scene, the killer's demeanor suggests that he encountered Phil in the restroom by coincidence and improvised the kill, rather than anticipating all of Phil's actions as part of a perfectly executed plan.
The general logistics and planning of the murder are a separate issue - because no, the murder was planned. The entry just says that it's "highly unlikely", putting it mildly, that the killer could guess the exact position Phil would pick to listen to the noise. Just a few inches up or down, left or right, make a huge difference. The killer looks at the knife admiring the results, because if he had any doubts that he got his victim, he'd be trapped in a bathroom with a screaming, wounded, angry Phil and plenty people who could come and help.
To be more clear, the correction here is that Phil had heard strange talking/whispering rather than music, which makes it at least a little more plausible the killer would think he might put his head up against the wall at a certain spot. Unlikely for sure, but unlikely isn't a mistake, it's just what movies do. Phil's death was planned yes, though it stands to reason the plan was more "surveil and strike when vulnerable" and less "wait for him in this particular stall we know he'll be next to."
Plot hole: The scene takes place in Julia Roberts' father's stable. Mel Gibson explains to Julia Roberts that he was supposed to kill her father, a judge, because he was going to reopen a certain case. Gibson says that he couldn't kill him and they became friends. He further explains that he was the one to talk her father into reopening the case in the first place. The problem is, they didn't meet until after he decided to reopen it, since that was why Gibson was supposed to kill him in the first place.
Plot hole: The use of massive explosives to separate a ship makes no sense as the explosion would send fragments at high velocity in every direction guaranteeing it would penetrate whatever ship is remaining. As we see in the final scene when the ship does blow apart, it is not a precise controlled detonation to sever connections but a total (and glamorous) explosion which makes no sense whatsoever.
Suggested correction: The explosions breach the outer hull, pulling the debris outward with the explosive decompression, the film shows the ring shaped explosions at both ends of the corridor. The debris wouldn't hit the lifeboat because it is heading in a different direction.
Plot hole: Regis could have saved himself a lot of time and solved the case much quicker if he had just verified the entries in Carla Town's day planner with the businesses listed. A few phone calls would have told him the entries were forgeries without going to the technician for help.