My client of 83 years old has vascular dementia - but our concern is his very frequent and very bad diarrhea.

Your client needs to see a board certified gastroenterologist.

Obviously, as I'm sure you already know, he needs to see his physician. Family pracitioner, geriatrician, or internist to start. A GI specialist, if no one can figure out the answer. Hydration and managment and monitoring of electorlytes is essential if diarrhea is chornic. Most common areas to look for cause, are meds- side effects, diet, food intolerances, new foods introduced etc, chronic contaminaiton of food, etc,  infection-viral, bacterial, parasitic, motility issues, parital obstrucitons, colitis, ulcerative, crohns,  A reaosnable family doc and certainly an internist should be able to figure most of this out, a GI specialist, would assess the motility issues rule out colitis, etc with more in depth diagnostic testing if it gets to that point, and the obvious causes have been ruled out.  Good luck Make sure he gets in soon.