Buck gashes his head open while disembarking the plane in the first book. He immediately heads to the terminal, bleeding from the head the entire way. After getting there and checking his e-mail, he thinks "Crap, I'm sure bleeding a lot. I'd better try to stop it, so I'll go into the washroom and try pressing wet paper towels up against it. Damn, it's still pretty bad. Oh look, here's a doctor with nothing better to do than stitch up bleeding guys in washrooms. Problem solved!" It didn't occur to me until a day after reading this that Buck must have passed lots and lots of medical personnel while walking to the terminal, any one of whom would have been quite willing to treat his wound. (After taking care of the more serious cases, of course.) But he just completely ignored them? And none of the EMTs noticed a guy with a severe head wound walking by and thought to stop him before he passed out from blood loss halfway between the plane and the terminal?
As the Slacktivist notes, the doctor who complains about being bored in an airport lounge while wrecked airliners burn outside is one of the most disgusting characters in the series. It would almost be Fridge Brilliance that he wasn't saved, except there's no indication that you're supposed to take him as anything but the kindly man he appears to be.
At one point in the story, it is noted that the American militia movement (whom the authors are, as expected, supportive of) is the ONLY force who are opposing the Antichrist when he calls for the world to disarm. Not only does this imply that ACTUAL armed insurgency/anti government groups throughout the world who actively fight government forces (Lords Resistance Army, the Taliban, Somalian insurgents, IRA groups to name a few) are suddenly more than happy to disarm when politely asked, but that that these same militia whom the authors like so much are not "true Christians" as not only were they not raptured, but enough remained for them to be a noted power.
The entirety of the Russian (and Ethiopian) armed forces attack Israel for little to no reason, get knocked out of the sky, and nobody does anything about it for a year?
How could anyone even investigate such an event? Would Israel have to possess such technology to be able to pull off a massive Curb-Stomp Battle that can only be attributed to God?
Freak weather blew all the bombs and planes off course? All the bombs were duds? That's probably how Nicolae and the media spinned it, just like how they spin every disaster in the tribulation.