I know that Alzheimer's damages a part of the brain called the hippocampus, which has a central role in day-to-day memory.
But, could it affect also on things in other memory centers, things such as taste and moves?
Oh, yes, though short-term memory loss is often an early sign.
"For many, decline in non-memory aspects of cognition, such as word-finding, vision/spatial issues, and impaired reasoning or judgment, may signal the very early stages of Alzheimer’s disease." from https://www.nia.nih.gov/alzheimers/publication/alzheimers-disease-fact-sheet. Warning: grim.
Whatever your brain does, Altzheimer's eventually undoes. For more details: http://www.alzheimers.net/stages-of-alzheimers-disease/