Why basement membrane thickens in diabetes mellitus?
The endothelial cells in small blood vessels take in more glucose (as glucose levels in blood are high due to diabetes.) Thus they form surface glycoproteins which causes the basement membrane to become thicker yet less strong. This leads to blood and protein leakage from the blood stream in other tissues in the space between cells. Blood leakage alters cellular blood supply for all cells.

Less blood means less oxygen and less nutrients. As you probably know nervous tissue gets damaged fastest without oxygen thus explaining diabetic neuropathy. Also retina and kidney contain cells that get easily damaged when there is not enough blood.

Probably the worst complication is neuropathy, because the person suffering from it may suffer a heart attack (caused by the accelerated process of atherosclerosis in diabetes) and feel less pain (http://medlineplus.gov). 

Collagen and laminin poduction increases as a result of the fibrosis process that takes place when a tissue gets less nutrients than it needs.

Diabetes affects all blood vessels, even the larger ones. See macroangiopaty.

From http://en.wikipedia.org/wiki/Microangiopathy