During the tug-o'-war between Pug and the Keystone Cops, Pug's boxing gloves disappear and then re-appear on his hands.
Fatty has a near-unlimited supply of bullets in the revolvers he fires during the finale chase scene. He has no capability, because of the boxing gloves he wears, to reload, nor was he carrying ammunition to do so.
Fatty Arbuckle's corner gets very slippery very fast after the second round (where he continues to slide out of this chair). It goes almost instantly from a limited slippery area around his chair to almost 1/2 the forward area of the ring. Possibly indicates numerous takes and re-takes, since he is sprayed with water by this supporting team, plus he drinks (and possibly spills, since he seems to nudge the bottle with his foot several times), what looks like milk during the intervals.
The sign advertising the Cyclone Flynn fights doesn't appear in front of the town hall when the two hobos decide to pose as pugilists (1min 55sec). The sign doesn't appear until 7 minutes into the film.