Avoiding simple carbohydrates (#1) is primarily important to control blood sugar (elevated blood sugar has many detrimental effects, both short term and long term [2]). But fructose and alcohol, also simple carbs, are metabolized by the liver and the metabolic by-products are shown to cause inflammation as well [3]
[1] http://www.ncbi.nlm.nih.gov/pubmed/21047463
[2] http://www.mayoclinic.org/diseases-conditions/diabetes/exper...
http://www.medicalnewstoday.com/articles/264164.php
Basically, people with poor oral hygiene are more likely to develop Alzheimer's than people with good teeth.
You might have heard about a similar study that found a link between oral hygiene and heart disease. The theory, at least in that case, is that bad oral hygiene causes chronic long-term inflammation throughout the body, not just in your gums. This might increase risk of heart disease. Without looking at the data, I would guess that the same theory applies to Alzheimer's and maybe other diseases. The usual caveat about correlation != causation applies of course.
Oral hygiene is a good proxy for people who know it's important, but somehow still forget. A solid proxy for executive functioning decline, executive functioning in general, working memory, and a cluster of other things.
Good oral hugiene reduced that.