Corrected entry: When the hotel staff burst into Kevin's suite, he plays back the gangster movie soundtrack, and it's directed at the nasty bellhop. The gangster reads off a list of people that this bellhop has supposedly been smooching with. When the gangster says Cliff, the tape stops because the old security guard is named Cliff, and we see his reaction. But Kevin could not have known this, or even that Cliff was in the other room, or when to stop the tape.
Corrected entry: There's no way Kevin could have known (when recording as his father) what the hotel reservation lady was going to say, but he got the back and forth dialogue perfect as a recording.
Correction: In these two films, Kevin is portrayed as being a pretty smart and even genius kid. And the way these play out, it requires a lot of suspension of disbelief anyways. This isn't really a mistake so much as an exaggeration of showing how smart Kevin can be.
Kevin may be smart, but the point is he recorded his dialogue as his father before the call was made. He didn't know what would be said in that exact order. The operator could have said any other question (date of travel, how many people, or any random information) or put Kevin on hold at the last second. No way he would know he would be asked about a "credit card" at that moment. That was the point of this entry.
Correction: Kevin doesn't stop the tape at "Cliff," he stops it at "I could go on forever, baby." There is a pause, but only in the dialogue of the guy on the tape. The fact that the bellhop was named Cliff is a funny (and intentional) coincidence.
Actually, Kevin stops the tape after "Cliff", and then after seconds go by where everyone looks at the guard Cliff, Kevin continues the tape where it says "I could go on forever baby." The fact that Kevin would even stop the tape after "Cliff" in the first place could be submitted as a mistake since he never met Cliff before this point and would have no reason to have stopped the tape there in the first place. The original recording of the movie had no pause between the two lines.