Recently, we've encountered a couple instances where iPhone users were having trouble getting apps to install properly. When they would try to download an app, the app icon would appear on the homescreen as usual, but it would get stuck in the "waiting" or "loading" process. And the issue would continue even if the users restarted the phone, deleted and restarted the downloading apps, or resynced the phone. Needless to say, this is pretty anoying, especialy if you're trying to download an app you want to use right away.
As it turns out, though, this bizarre issue calls for an almost equally bizarre solution. The cause of this issue lies within iTunes (on the iPhone, not on a connected computer). For some reason, if you have pending downloads in iTunes, these downloads prevent apps from downloading properly, hence the stalled app. If you run into this situation, here's how to fix it:
Open the iTunes app on your iPhone.
Select Downloads on the bottom navigation bar.
You'll see the pending iTunes downloads on the page. Swipe to the left over each of them, and clickDelete. (You'll be able to restart the downloads again from the Purchased menu in iTunes later.)
Go back to the homescreen, and your apps should be downloading.
We've seen this situation--both the problem and the solution--played out on various iPhone models both with iOS 6 and previous iOS versions. Feel free to let us know if you need help with it.