Nope, not a mistake if you listen closely to what Jerry says right before the part of the scene you posted.
First, he confirms that Newman indeed got his hotel reservation for "the millenium". (Newman: "...as a matter of fact, I *did*").
Jerry is simply pointing out that since "everybody knows" [including hotel reservation desk clerks] that the millenium doesn't begin until the year 2001, this means that unbeknownst to Newman he is in fact booked for the night of 12/31/2000, instead of 12/31/1999 when all the real fun will supposedly take place.
So the joke is that Newman is going to show up for his reservation on 12/31/1999, and find that he's exactly one year too early. So he'll have to wait a year for his reservation. Thus while everyone else will be whooping it up on 12/31/99, Newman's chronometrically-accurate "millenium party" won't be for another year (and thus, quite lame).
Lesson: Newman should've given an actual date for the reservation and not just simply said "the millenium" to the desk clerk.