I went through a little discussion with another guy who mixes where I work about monitoring at the mix position. While it's quite common for a monitor engineer to have a listen wedge or his own IEM so he can hear exactly what the artist is hearing, it's not as common for front of house.
The reason is that it's pretty easy to simulate the artist's experience. Joe Q Frontman is standing 2 feet from a wedge on stage, so the monitor guy stands 2 feet from a wedge by his mixer and they're both hearing pretty close to the same thing. It's a little more difficult to re-create the sound of a large PA in a booth.
That's the problem, as usual the mix position is crammed in about the least effective place it could possibly be. Not only does this guy have to mix pushed up against the back wall, but also encased in a small thatched hut with a couple tiny windows for him to peer out of. He's looking for a way to check the balance of things out in the room.
Let me interrupt here to say that despite being far from ideal, this is actually one of the better booths I've ever tried to mix from. To my thinking it shouldn't be that difficult to play some music and walk back and forth from the booth to the room until you understand how things sound comparatively. Or have someone baby sit the mix during a service and do the same thing with the actual program material.
Or, we could throw a decent pair of cans in there (for the layman: cans is a term for headphones that dates back to the days of telegraph operators when the old school headphones looked like cans of tuna on either side of the head). While the cans aren't going to sound exactly like what's going on in the room, neither is a wedge, and cans are a lot more discrete way to check on things than blasting away with a speaker in an enclosed space. Another thing to consider is cuing up playback material. It's one thing to get that next track ready in the cans, etc...
One last thing to think about. One of the major frustrations that sound guys have is slapping on the cans and having things sound nothing like what's going on in the room. So here's the trick. Play something back that you know well and EQ the room to sound as close as possible to that. Then when you line check your performers, use the headphones extensively. Then when you bring up your mix, you should hear something that more or less approximates what you just tuned up in the cans. The better job you do tuning the room, the closer it is.