You're the perfect person to ask then: a french teacher once told me that bilingual people develop memory problems in old age sooner than others. I'm not sure if he specifically mentioned Alzheimer's or not. Have you heard of this, and do you know of anything to back it up or refute it?
I have good news and bad news for you.
The good news is that, when it comes to Alzheimer's, being bilingual appears to be beneficial. A researcher by the name of Ellen Bialystok has looked into this question; in a recently published paper, she and her coauthors concluded that among people who have regularly used two languages for most of their lives, the onset of dementia is delayed by an average of four years. (By "dementia", I'm referring to severe age-related declines in mental functions, of which Alzheimer's Disease is the most common form. The Bialystok et al. paper specifically states that their conclusions hold true for Alzheimer's as well.) Note that they don't make any claims about whether this conclusion applies to people who learned to speak multiple languages as children but only use one in later life, or people who learned a second language as an adult and use multiple languages daily: those populations might benefit from a similar delay, but they weren't tested for this paper.
On the memory front, I don't know about age of onset, but bilinguals behave differently than monolinguals on memory tasks throughout their lives. Here, there's both (more) good news and bad news. (I'm going to be cribbing some of this from another one of Bialystok's papers, which, as with the paper referenced below, you'll probably need to access at a university to read more than the summary.)
Someone who grows up multilingual, while having the obvious advantage of being able to speak multiple languages, tends to be less proficient in each of those languages than monolinguals - that's one of the consequences of splitting your speaking and listening time between several languages. As a result, bilinguals tend to have smaller vocabularies (within each language) and perform worse on word retrieval tasks than monolinguals throughout their lives. So, bilinguals are worse than monolinguals at memory tasks that rely on verbal recall (e.g., "Memorize this list of words and then, in a little while, I'll ask you to tell me what they were.")
At the same time, there's some evidence that being bilingual actually helps you on other kinds of cognitive tasks. Bilinguals perform better at some tasks that place big demands on short-term memory, and, more controversially, on some tasks that require what we call "conflict resolution", situations where you have to choose between two or more possible responses (the Stroop effect is the most famous example). They're better at conflict resolution tasks, so the theory goes, because they've spent their whole lives choosing between multiple competing representations (one per language) for each word. The result of these advantages is that bilinguals tend to be better than monolinguals at nonverbal memory tasks (for instance, recalling an ordered sequence of blocks).
As for how these findings are affected by aging, I think that the relative deficits and advantages present in young adults should carry over into later life. For example, another researcher, Tamar Gollan, showed that bilinguals' naming deficits persist with age. If that's true, then while I don't know about age of onset, I would expect older bilinguals to have worse verbal memory, and better non-verbal memory, than their monolingual counterparts.