R1 on 2B and R2 on 1B. B3 hits to short left-center. The ball is fired to the infield but sails over everyone and stops near the offensive team's dugout area. F3 goes after the ball but slips, trips, falls, and twists ankle over some bats laying on the ground. By the time defense the can recover, R1 has scored with R2 on 3B & B3 standing at 2B.

Is anyone out? Who goes where?

No rulebook to refer to with me today, but here is my take under ASA rules.

Once F3 slips on or is hindered by the equipment left on the ground, the ball is dead, interference is called and the runner closest to home at that time is declared out. All other runners are returned to the base they last legally touched.

This ruling assumes that the bats left on the ground near the dugout are warmup or extra bats. If F3 trips over the bat that was used by the batter, play continues. This piece of equipment is where it was supposed to be, discarded on the ground after use by the batter.

If I am incorrect, I'm sure that my compatriots on the board will let me know! :D

Speaking ASA

Officially:

Dead ball. The runner being played on will be ruled out.

In this scenario, there was no obvious play on any particular runner, so all runners are returned to the base last touched at the time of the "interference."

Unofficially:

Now, if you're lucky, the defender will attain the ball and attempt to throw a still-moving runner out. Now you have a play and that runner should be declared out.