
Plot hole: At the end the police shoot Cole while he was chasing Dr Peters but the police do not stop Dr Peters and question him as to why a man was chasing him at the airport with a gun, instead he is unchallenged and allowed to continue his journey.
Suggested correction: There is no connection between Cole and Dr. Peters, nobody knows he is specifically chasing him. Dr. Peters is beyond the gates and on his way into the plane so unless they want to stop the entire flight, which is unlikely, he is left alone. Perfectly reasonable.
Cole is chasing a man and Dr. Peters is running away (and knocking people over in the process). Further, they were screaming "there he is...stop him he's got a deadly virus" and pointing at Dr. Peters. Highly unlikely they would have let the plane depart.
There was a dude with a gun, a lot of people were running, panicking. Perfectly reasonable reaction from Peters. The police were after Cole anyway, so the attention was on him, not on Peters. And as I said, Peters was already past the inspection, so he was where he was supposed to be and there was no reason to stop him.
Not to mention that Dr. Railly can also corroborate the reason Dr. Peters is being chased.
Dr. Railly can corroborate the reason Cole is chasing Dr. Peters. When she points out that he is even on the front page of USA Today with a Nobel Prize winner, I think they'd definitely investigate.
The shrink was still alive and seemed to give up quickly on her mission to stop a virus from killing billions. Like she just let them take her while she remained silent instead of continuing to scream that he had a virus so Cole died in vain. And they would know why he was chasing them because all they would need to do was ask him.
Her concern was with Cole, she tries to protect him throughout the movie. After Cole is shot she knows there is no way they let her continue the chase, all she cares about is Cole. Cole is being chased by the cops, no reason for them to believe what he is yelling, no reason to believe her either, since she is as an accomplice.

Plot hole: When Bo-Tat is purchased the Village Elder insists that Lihn go with Bo-Tat, it is CLEARLY established at this time that A) Lihn is an orphan and B) his parents were both killed in the war. For two-thirds of the movie Capt. Doyle repeatedly comments that Lihn can't be trusted because we don't know who (NVA or USA) killed his parents. There is no possible way that Spc.5 Farley wouldn't know this. However, halfway through the movie (on the river boat) he asks Lihn where his parents are and how they died. He couldn't possibly be ignorant of this, since he took part in at least two of the prior conversations.

Plot hole: Jose is the only one carrying the bag of money, then he gets killed, in the next scene Anthony and the others have the bag on the table though none of them were carrying one besides Jose.
Suggested correction: Kirby and Klingon were both running with bags of money.

Plot hole: When Sid shoots the TV-show host, the number of viewers doubles in two seconds. How would all those people find out so fast and switch channels?

Plot hole: Even though the Brady Bunch kids won $20,000 (check, not cash) in the "Search for the Stars" contest, they would not have immediate access to it, so would not be able to merely take the oversized representative check - which would be nonlegal tender - to pay for the taxes; they would have to wait until they received an authentic hard copy (real check) and wait until the check "cleared" the bank (was legitimate and payable). Clearing the check could take weeks because the Brady's didn't have at least $20,000 in their checking account to cover what could be a bogus check. (01:19:03)

Plot hole: All of Keslee's troops are spit and polish with nice uniforms, holsters and boots. But in the scene where Becca is pulled out of the pipe, one of them just happens to have a pistol in his belt for Keslee to grab and threaten Becca with. Very convenient.

Plot hole: The premise is that the back-story is a fabrication, including the five being placed together in the police line-up and in custody in order to get them to work together. But in the flashback of Keaton in the restaurant, it is Dave Kujan who takes Keaton in. It is inconceivable that Kujan would be complicit in the staging of the line-up (and doesn't fit with the plot). And if Verbal is inventing it, then Kujan is going to know it didn't happen. It doesn't make sense and undermines the plot.

Plot hole: Jamie takes off running with her baby. 33 seconds later, Michael kills the nurse. 30 seconds have passed since killing the nurse and Michael is right behind Jamie and somehow manages to find a knife along the way. All in a one minute 5 second time frame. (00:04:50 - 00:05:55)

Plot hole: When Injun Joe is about to kill Huck, Tom takes notice of the chest full of gold coins and then empties the chest out (offscreen) because it was too heavy for him to lift, and then tricks Injun Joe into trying to retrieve the empty chest, resulting in Injun Joe falling to his death. The amount of time that passes between Tom glancing at the chest and then tricking Injun Joe before he can kill Huck is roughly 5 seconds. There's no way Tom could have emptied out of the chest in that little amount of time if the chest was too heavy for him to lift in the first place, especially without making a sound.

Plot hole: After leaving the hospital, Racine ducks into a pachinko parlor. In there, he gets a young girl to help him find a telephone and a taxi. The problem is, she is about 10 years old, and you have to be 18 to even enter a pachinko hall. The attendants we can see in charge would have evicted her within minutes.