I'm really surprised this hasn't been brought up yet.
A few of the stages in 0.8 have parts of the stages where, if you stand there, the opponents won't go after you once you chase them.
The stages and parts include:
-Planet Zebes (the floating platform in the eastern-part of the stage)
-Bramble Blast (the two platforms on the right)
-Planet Namek (the two parts of the platforms opposite of each other)
-Mushroom Kingdom (the platform on the left)
-Fourside (the building on the right and the building on the left)
-Hyrule Castle (different from the rest, if you jump on one of the platforms on the tower, the opponent won't follow you and go under the tent and have strange AI)
-Saffron City (different from the rest, if you try to run away from the opponent then the opponent will walk, then stop, walk, then stop, until they get to you)
On a different note, the platforms in Pirate ship need to be coded to be longer. Currently, the sprite is longer than the place you can stand.
The reason why this isn't posted in the 0.8 bugs thread is that this is a much more urgent bug that should be fixed ASAP.