I thought that the only phone on the wife's plane belonged to the reporter guy. He was up there, talking to his media outlet and scaring everyone in the airport with his journalism, no? Then, Mrs. McClane (spelling?) busts into the bathroom and tases him I think. That's why the plane and its passengers were in danger, no?

no, she calls him in the beginning of the movie and also later from airplane phone

Oh Oops. Then, you got me without an answer, Markoff. Seems like a plot hole.

Barnes: "What about the airphone idea?"
ATC: "There's 18 planes up there. Only five of them have those phones. We got through to three of them. We're still trying on the others."

ATC couldn't contact two of the planes that had airphones (Airfones). Holly was probably on one of those planes.

Later they used an outer marker beacon to talk to all of the planes and warn them of the situation.

Side notes:

Interesting fact is that before 1992 airphones only permitted air-to-ground calls. As the film was released in 1990, it shouldn't have been possible for anyone from the ground to call the plane via airphone.

So, a factual error or was the whole incident set after 1992 when two-way phone calls were possible?

so they couldnt get in touch but she could call second time (or he calling her, dont remember) and TV reporter could call also without issues? that is quite a stretch to believe...

Well, airphones are known to frequently drop calls. It could be that under those extreme (weather) conditions only three planes could be contacted after awhile and they were still busy trying. There might have been less interference later when Holly and Thornburg used the phone. Then it wasn't necessary anymore for the ATC as they then used a beacon to communicate with the planes.

Of course you could argue that it is quite a coincidence that it was Holly's plane and another one that couldn't be reached immediately. If her plane was contacted, it could have been diverted to another airport. McClane would have less of an incentive to risk his life. Thornburg wouldn't have reported on the situation and cause panic in the airport, and we wouldn't have the satisfaction of seeing him being tasered by Holly.

This movie, as many others, does have its errors, plot holes and goofs, but it's still a great action flick.

I mean even the whole scenario with airplanes running out of fuel was very dumb, they have backup airports and if they can't land they will just redirect to other nearby airport, so there would not be really any time issue once they established beacon communication.

Whole movie seemed like very lazy writing after first Die Hard, which looks less dumb. Personally I like the most third one, going to watch on Christmas eve I guess despite different season in movie.