No, you can only plat the current day's games. I'd love to see this expanded in the future, but it is still a really nice feature.
At this point, there seem to be no errors or injuries. Injuries do occur while simming games, but not while playing. But there are no bobbled balls, and most every throw is right on target. there is some hope that this will be fixed in the upcoming patch.
Also, the franchise play is underwhelming. The stats do not sim well, and player fatigue seems to be poorly handled. I'm playing out a season, and it is fine from a gameplay point of view. The season presentation is really, really good.
It is frustrating that when you want to play a random game under Play Now, you cannot set the opposing team's pitcher or line-up.
I doubt the franchise gets patched up, and since 2K9 had the same issue with assigning opposing pitchers and line-ups, I doubt this is getting fixed either.
I can say that I have enjoyed the heck out of the game. It is a lot of fun to play.