Babies def pass Mucus through their bowels due to infection e.g Cold.
As it is a baby best to check with doc. It will also put your mind at rest
it may just be a sinus infection. sometimes a baby or a grown up even will pass mucus through the bowles. also when mucus gathers in the stomach it can cause some one to throw up. it makes you very nauseated. Your Doctor will probably perscribe an antibiotic for your baby.
Is your baby bottle fed or breast fed? Its normal for young babies to have stool that looks like butter in color. They also will spit up phlegm along with their milk after eating. Babies don't eat solid foods for several months, when they are only digesting milk or formula it going to look different. Drs won't put you in the worry too much catagory for bringing him in. They would rather see him then you not bring him in if there really is a problem. It could be something as simple as switching formula.