I, too, have not had a problem with the 1st baseman coming off the bag. I use the right stick to throw, though I'm not sure if that makes a difference or not. The 1st baseman has come off the bag once in my experience (within my first game or two).
Fielding flyballs has been a similar experience. I dropped one or two that I shouldn't have in the early going, in large part to not having a feel for how to field. I have had one drop since learning the game. It seems to happen when you fight the subtle auto-positioning when settling under a fly ball. That is, if the fielder is in position to catch and I toggle the left analog stick in any direction, it seems to increase the chance for error, even if the left analog movement does not yield a drastic on-screen direction change.
Even using Inside Edge, I believe the batter aggressiveness could still probably use a little toning. Though, truly, the Inside Edge is a great tool to use in the interim