There are certain behaviors dogs will use when they want the one they're communicating with (dog or otherwise) to understand that they're stressed, and to calm down, back off, and take it slowly. Turid Rugaas describes these, and illustrates them with fantastic photographs, in this book.
Some of these signals are subtle, and can be misinterpreted by we humans. If you give your dog a cue, and she starts sniffing around on the ground instead of performing the action, that's a little bit frustrating, yes? What happened on the ground that's more interesting than all of the training and motivation you've tried to instill? Well, "sniffing" can be a calming signal; your dog might not exactly know what you mean by the cue, or know why you're asking for it in that particular place.
Yawning is another one. Granted, not every yawn is a calming signal; Elka has a high-pitched, very loud yawn that she performs in which it seems as though her head has become entirely flip top. I call it her "Raptor Yawn". That's one that she does to get our attention, typically if she needs to go out, at which point I cue her to "tell me what she needs". I think a calmer (and quieter!) yawn is the calming one, used to diffuse overly exciting situations.
And, the last one I'm going to list here (you should really read the book, after all) is what Patricia McConnell calls the "tongue flip", and what's listed here as "licking the nose". Both amount to the same thing, the dog's tongue coming out at a stressful time. Even if you don't notice head turning, and slowed movement, watch, at least, for the tongue flip, as though you're watching for a white flag of surrender.
Sometimes our poor dogs just don't know how to deal with we humans and our wackiness, and understanding the body language that they use to communicate that with us is tremendously important. On Talking Terms with Dogs: Calming Signals is a very clear, if brief, window into the world of communication that dogs have, and I strongly recommend it.