Is drooling while and after eating a sign of swallowing problems?

Be careful that she is not aspirating her food, which can lead to pneumonia. Ask her specialist for advice.

The mouth/git is producing excess mucus . You might note which foods she has eaten when she has the drooling. The most common offenders are the foods unfortunately most the processed soft foods fed to the elderly....white rice dishes, wheat flour products & by products, any foods with a lot of sugars.. puddings, candies, ice creams...& all manner of sweet treats.
This causes an acid condition in the gut, which in turn causes irritation. The irritation leads to inflammation...And the secretory glands overproduce mucus to dilute the offending foods.
Does this make sense?
..having dessert after a meal causes the meal to ferment...just as ice cold water (an american habit) inhibits the digestion.
It all comes back to the gut...and what one puts in it.
A healthy diet is rich in fruits vegetable grains seeds and nuts....in their most wholesome organic form.
A 1Tblspn Raw Apple Cidar Vinegar
1Tblspn Raw honey (from your area)
1/4C warm distilled water
Stir well & have her drink before each meal. Tastes pleasant
This will improve her entire digestive system remarkably
This will stop the drooling episodes

Yes, she could possibly have Dysphagia - a swallowing problem.

Drooling is one of the signs - but I am not a doctor and drooling could be symptomatic of other disorders as well.

My mother all of a sudden would foam at the mouth after eating. They gave her suction. This started after a high lactose meal in the hospital, grilled cheese, chocolate milk and pudding. I told them she couldn't do lactose, but had not ordered her dinner that day, because she was supposed to go to rehab after having broken her pelvis. They gave her a swallowing test, but the problem persisted. She ended up in the ICU where they put her on a breathing machine that breathed in and out. She hated it. She had Alzheimer's, and a nurse said, "Be careful of putting her on the medical merry go round." She had a living will and did not want to be hooked up to anything. She ended up in Hospice where she lived for 8 more days. She was 90.

She needs to be evaluated by speech therapist

Mom is 86 and as Long as No Problems with Dysphagia (Swallowing) Which needs to be Kept an eye on, Then it is Normal for her to Drool at her Old Age.

Could this be a medication side effect?

Might be. A speech/language specialist with CCC and training in geriatric/swallowing issues could tell you for sure. Also might be related to advancing Parkinson’s.

Thekay, sometimes acid reflux can cause drooling when sleeping but usually one gets a really heavy acid taste in their mouth.

This does sound very much like she is having trouble swallowing her food and some of it is ending up going the wrong way, which besides being distressing could lead to aspiration pneumonia. She needs to be evaluated for dysphagia, is she on a modified diet at all?