Hi and welcome to BPO! I'm Stephanie, mom the the goofball in my avatar, Sierra. She's a 5 1/2 month old Newfoundland and the light of my life. We have many other pets as you can see in my signature below, but Sierra is the reason I ended up here at BPO.
Sierra also gets things caught up in her lips - food, tissues, dirt, leaves, sticks, cat litter...whate ver she's been chewing on, which is pretty much everything. All of it ends up in her water bowl when she drinks along with a healthy dose of slobber. I've never owned a Mastiff, but I can say, the hose idea is a good one. Sierra will drop EVERYTHING and come running when she sees the hose is on. Other than that I just change her water endlessly throughout the day.
I would guess that drinking their own slobber and pieces of food is fine for them. Whenever she can sneak it behind my back, Sierra is perfectly happy drinking from our slimy frog pond and she hasn't gotten sick yet. I have had to fight to keep my lunch down a few times, but she seems to like it!