Gus is so cute in his pajamas!
I always try to clean up the vomit before a dog can re-ingest it. First, because I need to see if there is any obvious cause for concern - blood, foreign objects, noting color. Secondly, because whatever caused the dog to expel it might be because it caused irritation or gastrointestinal upset in the first place and his/her system needs to relax. If you can't get it before the dog, I'd suggest just stay observant of him/her. Here's an articles written by vets that may help. http://www.petmd.com/dog/emergency/co...dgvomiting
My issue is usually Thing 2 eating Thing 1's vomit. Dogs are gross!
Like Deb said, it depends on the situation. Generally it won't be a problem, but you might miss important health cues, and if he's eaten something toxic that has caused the vomiting, reingesting it isn't the best.
There should be no concern really (other than grossing owners out), but the issue is that many dogs who vomit will vomit again if the ingest anything afterward. More than being worried about eating the vomit, I would be concerned why the dog vomited in the first place. Did your dog vomit or did he actually regurgitate? Usually, dogs will readily consume regurgitated food as vomit often tastes very acidic. Here is a guide on telling whether a dog is vomiting or regurgitating: http://www.dogsupsetstomach.com/symptoms/dog-regurgitation/ (http://www.dogsupsetstomach.com/sympt...)
I visited this link and found another that is helpful here re. what to look for in vomit. *Caution: do Not read while eating. http://www.dogsupsetstomach.com/diagnosis/what-vomit-sample-tells-your-vet/
I notice that when one of my two dogs (brother and sister from same litter but couldn't be more dissimilar) , almost always the male, it is shortly after eating and he eats so fast that his sister rushes. On the rare occasions he vomits, he eats that up as fast. Nothing odd in the vomit. Just food