Revealing mistake: After Fin, Martin, and the rest get what they need in the Times Square area, they get in the cab and drive off, and just as we hear on the news "Moments ago the water spout came ashore and devastated the UN," in this exterior shot we can see the taxi's back tire as it's driving down the street, but the tire's not actually moving. Presumably the taxi is on a flatbed being driven by crew while filming from this angle, hence the tire being stationary.
Revealing mistake: When the stewardess asks April to sign her copy of the book entitled "How to Survive a Sharknado and Other Unnatural Disasters..." it's a thin book, and in the closeup as April autographs the page we can read the text and it's actually one of the versions of the "Samsung Galaxy Tab...For Dummies" book, not April's book. Also notice when Kelly Ripa shows April's book to the audience, it's now at least 4x as thick.