Goofs

Applied Cryogenics is part of "Old New York" and therefore should be buried under ground when Fry is unfrozen in year 3000 in "New New York".

When in the back room of the head museum, Bender pull out two bars to make an escape. But when he lifts them in triumph of his new options, in the window behind him the bars are back in place. On the next "shot", they're gone again.

When Leela calls for backup, her Wristlojackimator is on the wrong wrist. This happens when Fry and Bender are in the bar.

As people in (Old) New York count down the final seconds of 1999 (in the dark), the Earth's globe seen from outer space is shown briefly. However, the American continent is lit and moreover the orientation shows it is morning in the Americas.

This episode portrays both 1999-12-31 and 2999-12-31 as "the eve of a new millennium". This is a common misconception; historical epochs traditionally have no year zero (the practice of starting an epoch at 0 instead of 1 came in in the 20th century, but the Anno Domini Epoch was established in 532 AD), so the correct dates for these landmarks are 2000-12-31 and 3000-12-31 respectively. (Those who claim that "the Third Millennium started on 2000-01-01" are in any case trying to have it both ways; they're counting years from 0 but centuries and millennia from 1.)

When Fry goes into the Cryogenic Freezer, the timer is set for 1000 years and goes in on January 1, 2000. Fry then comes out on December 31, 2999 instead of January 1, 3000. Evidently the timer has no notion of the current date and thus cannot determine whether it is a leap year. The solution is to count a year as 52.1775 weeks or 365.2425 days, the mean Gregorian year. 52.1775 weeks times 7 days times 1000 years equals 365242.5 days. Therefore December 31, 1999, 23:59, plus 365242.5 days equals December 31, 2999, 11:59 (just before noon, i.e. in line with that Fry wakes up at daytime).

It's dark outside in New York at midnight when Fry is frozen, but a long shot of the planet actually shows the eastern half of the United States as being in sunlight.

The start of both the years 2000 and 3000 is heralded simultaneously across the globe. The midnights should be staggered due to time zones.

Fry mentions Star Trek, even though it is illegal in to say it in the future. So he should get arrested but doesn't.