I agree with Northern about the use of flash nosebands, which just conceal the issue of the horse not accepting the bit. It goes with the whole relaxation thing I was talking about earlier. Obviously not always, but often, a horse who is trying to evade the action of the bit, which is what they are doing when they gape their mouth, put their tongue over the bit, etc., is certainly not one who wants to relax into the contact. One of the fundamental principles of dressage (and mind you, not one enough people follow) is relaxation and acceptance of contact. One of my rants about dressage shows, at least in the States, is the way many judges are more inclined to reward a tense horse with a lot of natural self-carriage, fancy paces, and who can kind of fake a frame over a significantly less fancy, but relaxed, happy, and correct horse, especially at the lower levels. Anyway, one of the movements in American dressage tests (I've never looked at one in the UK, but it would shock me of this weren't on it) is the "stretchy-chewy" circle and the free walk, where you show the judge that your horse is in fact relaxed by lengthening the rein and he should stretch down and relax his stride. You can get this by putting on a flash, which limits the ways in which the horse can evade the bit, but in my experience horses have gone a lot better when I've dropped the flash and worked on true acceptance of contact.
I guess if I had a horse who got really explosive and who needed to be ridden dressage in a flash or it would spend the whole time going around with its mouth open avoiding the bit, I'd also be trying to work out what was going on with the horse. There are things you can't know, or do anything about even if you did know, like whether the horse is jealous if its regular rider's other horse, so the best I could do is tackle the things I do know and can do something about, like work on acceptance of contact and general relaxation.