Blood in any amount in the vomit can indicate poisoning when coupled with bleeding from other orifices. You will want to keep an eye on this as it is a possibility.
The most common reason for blood in stools is parasites such as worms or a protozoan infection such as coccidia or giardia. In severe cases there will be vomiting as well. Other causes for a bit of blood would be hard stools which can cause some bleeding.
The most common worms found in dogs are:
Roundworms, Hookworms, Tapeworms, and Whipworms and Heartworms
In some cases these worms are passed from the mother to the puppy, in other cases such as tapeworms, they are contracted by other methods such as ingesting an infected flea. Most over the counter medicine will only kill one or two types of worms, so your best bet is to take a fecal sample to your vet to determine the type of worms your dog may have and then decide on treatment. Dogs should be checked for worms periodically even if they appear healthy. This is so if your pet does become ill, you are not fighting a worm infestation along with a more serious problem.
For additional information about worms, see this site
Common dewormers are Panacur which is a prescription product so you need to obtain it from your Vet and it works on roundworms and whipworms. Wormers labeled as Pyrantel Pamoate are the best over the counter medication for roundworms. Drontal plus is also a prescrition product and is used for the treatment of Tapeworms. Revolution and Interceptor as well as other heartworm medications also control whipworms and roundworms. Another reason to keep your dog on Heartworm medication.
Information on coccidia
Symptoms are diarrhea which could be mild or severe depending on how infected they are. If severe there may be blood and mucous along with vomiting, loss of appetite leading to dehydration.
Information on giardia
Symptoms of giardia are diarrhea with possible terrible smell, mucousy stool and sometimes bouts of vomiting.
The following sypmtoms should trigger an automatic trip to the vet:
If your dog has acute vomiting and diarrhea lasting over 24 hours.
if your dog becomes dehydrated. You can tell by pulling up the skin between your dog's shoulder blades and seeing if it flows back down normally. If it stays tented or is slow to return to normal, your dog is dehydrated and needs fluids immediately and should see a vet as soon as possible.
If your dog's gums and tongue become pale and not their normal pink color.
If your dog's rectal temperature is over 103F (101-102.5F is normal)
If your dog becomes lethargic and non responsive.
If your dog has trouble breathing.
Hope this helps.