[MikeStrybel]

Here are a couple to consider:

Two outs. B9 bats in place of the proper batter, B8, and grounds out to end the inning. The defensive team did not notice the improper batter and leaves the field.
a.The defensive team can appeal batting out-of-order from the previous half-inning if the next half-inning hasn't started.
b.B1 is the batter that should be leading off the next inning if there was no appeal.
c.B9 should be the next proper batter to lead off the next inning.
d.If B8 leads off the next inning, B8 is not batting out of order.

I know this should be easy, but I have thought about it too much!
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R1, R3, one out. The batter's line drive is caught by F1. Both runners are moving on the pitch. F1 sees that R1 is way off first base and leisurely tosses the ball to F3 to double up R1 for the third out. While this is taking place, R3 has touched home plate prior to the third out at first base. The plate umpire waits until both teams have completely changed sides and awards the old offensive team a run.
a.The plate umpire awards the old offensive team a run and the inning continues.
b.The previous defensive team's coach can have a valid dead-ball appeal to negate the run.
c.There is no score on this play, the inning is over.
d.The previous defensive team cannot appeal because they did not do it before all infielders left the field and the catcher had left the dirt area around home plate.

Timing play? If the players all left the field there is no appeal.

Thanks for the advice.