All that remains after today is to place a steel beacon on top of the spire to raise the building to it symbolic final height of 1,776 feet.
Then again, the distinction all depends on your definition of "tallest." There have been numerous debates over the years about what you should measure, where you should measure from, or if certain structures can even be called "buildings." There are different records for the "architectural top," "highest roof" and even "the highest occupied floor." Though sometimes people can't even agree on what is a "floor" is. (Officially, 1 WTC will have 104 floors, not counting the multiple basements.)
And don't get started on measuring from sea level.
Thankfully, the Burj Khalifa is so much higher than every other structure on Earth (it will still be nearly a thousand feet higher than the finished WTC) that all its records are still safe, and there's no real debate about who is the king. For now.
UPDATE (10:38 a.m.): Today's spire installation has been postponed to due inclement weather in New York City. Looks the record will have to wait until later this week.