Corrected entry: When the President and Duncan's dad are looking for Hallie and Duncan, they see a couple making out. They stop them because the girl was wearing a pink dress, like Hallie's and the guy was wearing a leather jacket, like Duncan's. But how would the dad's know that they were wearing that if they left the house in something different and bought the clothes on their date?
Corrected entry: When Hallie and Jason are on their way to the dance they have to stop due to a flat tyre. Then it shows Jason asking a homeless man where Hallie went. He then goes into the pool hall and finds Hallie potting the first ball in the game of pool. She claims that she just left to go to the bathroom. This doesn't give him much time to change the tyre, but the tyre is fine when the car thieves steal it, they are able to have a high speed chase in it and drive around for a long tine.
Correction: First of all, Hallie's date name is not Jason, it's Duncan. Before Duncan asked the homeless man, Duncan was putting a tire against the side of the car and there was another tire already in place of the punctured one. Hence, there should not be any mistake in this scene regarding the tires.
Correction: When the President and Duncan's dad are looking for Hallie and Duncan, they do see a couple making out who are wearing clothes similar to their kids. However, that is not why they stop them. This is because, obviously, like you said, they saw them wearing different clothes. The President and Duncan's dad stop the couple (mistaking them for their kids) because the girl and boy have similar hair color and styles to Hallie and Duncan, respectively. They also have similar body types, and the dads just see backs and backs of heads.