So right after I posted last on Friday, I went on a ride and the chain dropped off the small ring one time when downshifting. I tried adjusting the low limit screw with the chain on the small ring and large sprocket according to the Shimano FD-5700 tech documents. But then Saturday during a 40 mile ride it dropped off the small ring once again. Right after the ride I went to the LBS and explained the problem, and also the issue of the RD hesitation when upshifting to smaller cogs. So the first thing he did was check the RD hanger alignment, and found it was out of alignment a bit. He got that lined up, and then went on to the FD - adjusted the lower limit screw and also lowered the FD clamp on the seat tube just a bit to get it closer to the big ring teeth.

Haven't really had a chance to ride the bike since then, so we'll see how it goes on the next ride.