[greymule]

an outfielder catches what looks like the 3rd out, and while enroute to the dugout he stops to brush off the base, which was previously missed by the runner

Actually, in this case the defense would still have to appeal to the umpire. This missed base would not be a force play after the fly out, so the "accidental force play" would not apply.

Here's an example of the AFP: Abel on 1B, Baker singles to right. Abel slides safely into 3B but missed 2B. F5 nonchalantly places a tag on Abel anyway. Abel is called out on the AFP for missing 2B.

Or: Abel hits an inside-the-park home run but missed 1B. Abel scores and F2 immediately hands him the ball as a souvenir. Abel is out on the AFP, since F2 "tagged" him. (Save your breath, guys. I know the miss at 1B is not technically a force play.)

We (at least) once had a long thread about just at what point the AFP no longer is in effect. Apparently, the end of "continuing action" voids the possibility, but of course that term is not precisely defined.