Corr i have just googled foods harmful to dogs and found a few i didn't realise, i have always given carrots every now and then to clean teeth, but apparantley veggies aren't good for there digestion!!
Carrots are fine - a bit high in sugars so not to be given in bulk - but perfectly safe. Dogs have a short digestive system and find it very difficult to break down cellulose, so veggies are best given pulped to enable them to get the benefit of them, and not just pass them out virtually unchanged. :)
I've always given my Lab carrots too but she's 13 now and having trouble digesting them. They're making her vomit. I've switched to bananas and cored apples as regular treats. The carrots were nice though as they gave her some good chewing.
One of my earliest memories of dogs in Sweden (before I was a dog owner) was taking part in a pet day and watching a demonstration of a Golden that was seeking mushrooms. VERY common thing to teach dogs in Sweden, to find mushrooms (or more usually chanterelles) for the owners to pick and eat! You can go courses to learn.