I started out shooting with my L eye closed (R eye/R hand dominant). It wasn't until I actually started shooting trap that I realized what a disadvantage I was putting myself at.
It took some practice, but eventually my scores improved dramatically by shooting with both eyes wide open. I carried this over to all shooting - pistols, SGs, bows, rifles, everything. I find target acquisition to be MUCH faster. And with practice, I shoot much better with both eyes open.