As Jim is listening to the mission briefing tape and as the tape is playing the first view shows the recorder with the cover off, but as views switch, there are 2 views where the cover in on the machine, then off again.
When the tape is self-destructing the reels are of a different type and it is an entirely different tape recorder.
As the recorded message for Jim is about to end, the left reel is nearly depleted of tape while the right reel is almost full. In the next scene when the tape is self-destructing, both reels are nearly equally full.
The real number of the bus (5307) can be seen above the windshield at the end when Phelps reveals he has the list.
A wide panoramic shot at 40:43 of the partygoers dancing is repeated at 41:16. The first few seconds of the pan--which would have included Paris and Dana--is omitted the second time, but Jim is visible in both shots, despite having left the ballroom after the first one.
When Wily steps off the elevator, you can clearly see that the floor is continuous, revealing that this is not a real elevator as it would be impossible for the elevator to move.
At the beginning an agent is able to record Vanin talking on the phone to his wife using a special microphone. The problem is that it also records what the wife says; this shouldn't be possible since even someone standing next to Vanin would not have been able to hear what she said.
Dana goes all the way to the EERP only to dress like Mrs Vanin just in case she has to fool a public servant.
It seems odd that it didn't occur to anybody to ask Vanin about the three numbers he told his wife on the phone. Doing so would have triggered his memory of the location of the microfilm. Even if he wasn't willing to tell them, they could have then used the usual truth serum protocol to get them the information and saved them the hassle of evacuating the embassy.
After Mishenko and the Vanins realize the Americans staged a hoax, Vanin insists he hypnotized himself and declares he did not divulge the location of the list. In Mishenko's office, he asks his wife to reveal the numbers he asked her to remember just prior to his arrest. He recalls what the numbers mean and blurts out they are a bus number. Mishenko and the Vanins being experts in intelligence matters, should have clearly known the Americans would have installed a bug in the room.
Mishenko should have realized something was amiss when the trucks blocked his view of the embassy. The first time he may have thought it odd, even though he would have seen there were no cars preventing the truck from pulling further up to the intersection.
But when the exact same thing happened again later, that should have been a red flag that something was going on.