Im talking about when the hotel near the end of the film. They never explained what happened to his credit card. He coyld have use it to get a room.

they were out of rooms, remember, that's why they had to share the last room

The better question is what happened to Dels Credit Card?
He had one so why didnt he use it at the Hotel.

He had no way of knowing how the switch occurred.
You're not real quick are ya?

I don't even think they all knew it happened. I didn't really think it was the manager's fault. He processed the cards and then set them back on the counter. Neal took Del's and didn't even look at it.

LOL, oh I forgot about that. I was watching it aghain ands havent got that far yet. Well why does he get mad at del in the first place it was the managers fault

Wasn't brought up again?? It was the crux of several scenes later in the movie. Del almost kills them by driving the wrong way on the freeway, then his lit cigarette causes the rental car to incinerate. Neal thinks it's funny because Del's on the hook for the cost of the car, but Del is forced to admit that he used Neal's credit card to rent the car. He thought that Neal had put it in his wallet out of "kindness"! Later, at the hotel, Neal's so angry that he refuses to allow Del to share his room so Del's forced to sleep in the snowy parking lot until Neal finally has a change of heart, allows him in the room, and from then on they're nothing but friends.
All of that hinged on their credit cards getting mixed up.