Is it common for people with Parkinson's and dementia to have a lot of saliva yet difficulty swallowing?

Answer to your question is yes. Do more research on Parkinsons and you'll find a lot of symptoms

Sometimes this can be a symptom of dysphagia (swallowing difficulty), there isn't more saliva than usual they just can't swallow it like we all normally do. There are meds that can dry it up but they can cause unpleasant side effects, if it's really bad you might need to keep a bib or towel tucked around the neck and protect the face with a barrier cream - the silicon ones like barriere (https://www.agingcare.com/products/wellskin-barriere-silicone-skin-cream-433861.htm) are not as noticeable as zinc based ones.