I've had productive phlegm (thick, mucus y) for more than a month without a cough. Should I be concerned? Any possible causes?

Possibilities... This may be due to chronic bronchitis, especially if you have smoked. An evaluation by your doctor is needed to find out if there are any associated symptoms and so proper testing can occur. Once you are properly diagnosed, treatment can begin. If you currently smoke, you need to stop. Your doctor can help with this as well.
Chronic bronchitis? Mucus usually comes out when you cough. Chronic cough with phlegm indicates chronic bronchitis. If you are not coughing, it might be coming from the sinuses. Talk to your doctor about it.