Most dogs have an upset tummy - loose bowel movement - at some point, often due to something they have eaten.
However signs for concern are bloody diarrhoea and/or vomit, copious amounts, as this sadly can very quickly be fatal, especially in very young or older dogs. Also if they are "flat" ie not moving about, not really responsive. These need URGENT veterinary attention.
If they are puppies or oldies speak to your vet for their advice. Anything going on beyond 48 hours requires veterinary attention.
If they are also foaming at the mouth, fitting etc as this could be signs of poisoning - this needs URGENT veterinary attention.
If it's just a dietary upset then they can have very loose stools but at normal times and are otherwise fine. With diarrhoea they usually feel poorly and sorry for themselves.
This a great website with photos of diarrhoea it's very helpful to explain to the vet what you are seeing and also gives an idea as to what is wrong
Undigested food material in poo is a cause for concern and may indicate several health issues, also if the dog is losing weight and trying to consume their own poo. Carrots, sweetcorn, baked liver treats area few of the items that tend to pass through undigested so are generally not a concern.
The best thing usually is to starve them for 12-24 hours but make sure they are drinking, you can get rehydration sachets from the vet .
For my dogs I use something called Norbrook liquid life aid which is a rehydration fluid for livestock you can get it from your vet or an online pharmacy such as http://www.hyperdrug.co.uk/Liquid-Li...ctinfo/LIQ960/
[I know that some people take it to help with a hangover, also after diarrhoea! but obviously not something we can advise upon ]
After really bad diarrhoea, when you reintroduce food, do it very gradually - vets usually recommend something bland like boiled chicken or white fish and rice, or white pasta if they won't eat rice, just a dessert spoon at a time to start with [presuming your dog is not sensitive to these ingredients]. You can put some of the broth in with it - also a sprig of parsley in with it to replace vitamins [but watch that they are not dehydrated as parsley is also a diuretic] You can add the parsley to the water to boil the chicken then add this as broth.
If you normally feed raw food, then do not give COOKED chicken as they may find it difficult to digest. I use plain minced raw chicken [which has been frozen for at least 2 weeks to kill off parasites]. Always handle raw food sensibly.
If your dog is producing poos with a sausage-skin-like coating, which is actually mucus, this is an indication of irritation, the stomach produces extra mucus to try to coat the lining to protect it. So this isn't something that should be ignored.
If in any doubt, telephone your vet.