Yes, exposure to light does break down Vitamin A. In addition, UV light can cause oxidation of fat causing slight changes in the flavor of milk.
A study done at Cornell University (L.J. Whited, et. al. 2002, Journal of Dairy Science, Vol. 85, Pages 351-354) showed a 32% reduction in Vitamin A in skim milk (in clear gallon containers) after 16 hours of exposure to florescent light of an intensity similar to grocery store lighting (1000 lx). Reduced fat milk showed a reduction of 24% and whole milk did not change. Brighter light and longer exposure times result in greater reductions in Vitamin A.
Vitamin A is a fat soluble vitamin and it seems that milk fat protects the vitamin from breakdown which is why there is more reduction in Vit. A in Skim milk than whole.
Trained tasters were able to detect an off flavor from light oxidation of fats in whole milk after 4 hours of exposure to light. It took longer to develop off flavors in skim milk (less fat to oxidize). Note these were trained milk taster, most people probably would'nt notice.
The old paperboard milk containers provide protection from light. More of the milk processors are moving to colored gallon jugs or to including a UV blocker in in the polyethylene jugs.
So, if you want the absolute best, buy your milk in opaque containers. Or, do what I do, don't worry about it and buy whatever is on sale.