Just saying 'Alzheimers' is an oversimplification.
In fact, a major type of dementia often lumped with Alzheimers is vascular dementia - it is this latter disease that has a much closer link to T2, since the causes of the protein tables that are associated with Alzheimers are still poorly understood.
The first connection is from the same cause as other circulatory problems that poorly-controlled T2s may face like kidney disease, strokes, heart attacks &c.
The other cause is more subtle - a number of recent studies have found that there is a link between certain vitamin deficiencies - particularly B6, B12 and folate and vascular dementia. Google for b6 b12 dementia and oxford university will find a recent one; supplementation has a marked reduction in neurodegeneration.
Wikipedia has this to say (well down the page) about B12 / Metformin:
http://en.wikipedia.org/wiki/Vitamin_B12
The initial drug of choice in T2s is Metformin and it seems that Metformin can lead to a reduction in 'intrinsic factor' in the gut, this can lead to poor uptake of these vitamins.
Research continues, but it seems not a bad idea to think of B6/B12 and folate supplementation if you take Metformin - particularly as you get older, since intrinsic factor output tends to fall with age. Calcium supplementation also helps. I'm sure there are plenty of people that have enough in their diet already, but since many T2s are trying hard to lose weight and improve their IR, a dietary deficiency becomes a bit more likely.