Vomiting: A common problem for pets is vomiting and diarrhea. Any vomiting pet must be evaluated for dehydration. If your pet is profusely vomiting (i.e. every few hours), then they are getting dehydrated and need veterinary care.
Australian Bulldogs seem to vomit often. Younger dogs will vomit a clear frothy type vomit, this is clearing the way and in anticipation of food. Adult dogs seem to get excited or first thing in the morning have a vomit. Maybe that is a result of some of the rubbish they have eaten the day before. I would never panic for one vomit!! Repeated vomiting is another story and usually a sign of something more serious. One of my dogs suffers Pica, a mental disorder that the sufferer eats what is unfit for food. But in my experience most dogs do this to some extent eating faeces, sticks, charcoal, etc. My dog has a penchant for small stones and became very ill with alot of slobbering and continual vomiting. It was easy to see the cause with 8 stones in the vomit.

Diarrhea:Diarrhea can be caused by a number of different things, from garbage, to parasites, to infectious agents (such as parvovirus). Most cases of diarrhea respond to symptomatic treatment at home. The most effective one is 24 HOUR FAST. Stop putting food into your pet for 24 hours (Day 1). This allows the intestines to rest and regenerate. Always have access to plenty of fresh water. After 24 hours introduce a bland food for the next 24 hours (Day 2). Plain white cooked rice, feeding equivalent cups of rice as their normal diet.
Most vet visits are for vomiting, diarrhea and itching/skin issues. I believe that if we can learn how to deal with these occurences correctly then alot of vet visits can be avoided. Like I said with either of these things I would straight away take the dogs temperature and go from there. If repeated vomiting I would seek the vets advice.

Constipation: There is 2 tell tale signs here. If your dog tries to push repeatedly and nothing comes then it is constipated. An emergency sign is if the dog cries or lowers it's hind in pain. This means something is hurting it and that could be a bone or stick! Emergency vet attention is required here.
For a blockage there is a method to try and that is paraffin oil, 10ml every 2 hrs. But in my experience that rarely works and an enema by the vet is the quickest and safest way. I have had a smaller Australian Bulldog girl get a chicken neck stuck. I no longer feed my dogs these but once or twice a year I will by for a treat and cut them in 3 pieces.