If my baby’s nose has been runny for a week, should I call the doctor?

Not necessarily. Most colds last 7-10 days. If baby doesn't have a fever or trouble breathing, and has been peeing normally (even if eating/drinking a little less), s/he may not need to be seen. Unfortunately we don't have treatment for runny noses, although nasal saline drops and bulb suctioning can help baby feel better. If you have concerns, though, your doctor is happy to check her/him!
Not necessarily. A typical cold or upper respiratory infection can take 7 to 10 days (rarely as long as 14 days) to resolve, and colds do not benefit from antibiotic treatments. So, it is not necessary to call your baby's doctor for a week of runny nose. However, if there are other associated symptoms (high fever, bad cough, difficulty breathing, wheezing), then of course it would be important to see the doctor.
Colds. Yes call to see if your child needs to be evaluated. Might be a simple cold but colds can turn into ear infections, wheezing and other conditions.
Not necessarily. Runny nose is so common in children as they meet the rest of the world. If the baby is otherwise comfortable, able to breathe, eat, and sleep, it is unlikely to be anything serious. Never feel silly about asking your doctor, however, especially if this is your first child or your baby is less than 4 months old.
Maybe. If your baby has other symptoms like wheezing, difficulty sleeping, vomiting or poor feeding then she needs to be seen, otherwise I recommend waiting for 2 full weeks before being seen.
Should see a doctor. A new baby (under 3 months) should see a doctor if there is a runny nose or other cold symptoms. Older babies with cold symptoms, but who are still happy and are eating fine, can stay at home for a few days under the watchful eyes of the parents. If a baby has been ill for a week, a doctor should check him over to see if there is something more serious.
Perhaps. Runny noses are very common during baby's first year. Most often these are of viral origin, which are self-limited. Usually saline drops and gentle suction are adequate for symptomatic relief. However, if baby displays fussiness, fever, sleeplessness, worsening cough, or diarrhea then concerns of possible ear or throat infection must be considered, triggering a visit with your pediatrician.
Call the doctor if. You should call your baby's doctor if the runny nose is interfering significantly with your babies ability to eat or sleep, seems to be affecting his/her breathing, or is associated with pain or fever. A runny nose alone, in an otherwise well baby, is not dangerous. The color of the nasal discharge is not really significant either, in most cases.