Is it possible to misdiagnose someone with Alzheimer's or dementia?

Of course it is, depending on how carefully and thoroughly an examination was done. A 15 minute mini mental exam can be very informative, but it doesn't take the place of detailed cognitive exams and brain scans such as MRI's and PET scans.

Yes. A person could have a temporary and reversible condition like a UTI or Normal Pressure Hydrocephalus.