Does Alzheimer affect more than day-to-day memory?
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/