Count Baserunning Mistakes as Errors Against the Batting Team
The 2009 playoffs (specifically the two American League qualifying series involving the Yankees) featured baserunning errors that cost the teams (the Minnesota Twins and the California Angels) outs and runs. Why aren't these counted in the stats? They are unforced errors like fielding errors. Similar to fielding errors, they relate to potential outs. In the case of fielders, it's outs that could have been had or an extra base or two they could have prevented the runner(s) from taking. Baserunning mistakes lead to either outs that shouldn't have happened, or bases they could have taken/runs they could have scored.
Some evidence suggests that Bill James is all over this.
Fielding Errors Due to Umpiring Mistakes
Baseball is a quick game, and umpires sometimes miss calls. They call 'em as they see 'em, but sometimes they don't see 'em. So when, for example, a first-baseman grabs a ball thrown off the basepath by the second baseman, tags the batter-runner on the first base line before he, the batter-runner, touches the bag, but neither the home plate umpire nor the first base umpire sees this. The official scorer usually assigns an error to the second baseman or (rarely) the first baseman. Why? If replays show he would have gotten the out, then it needs to be called something else. An example might be drawn from a strikeout where the catcher drops or misses the pitch, and the batter-runner moves to first base. The pitcher still gets the strikeout but no out gets counted. Maybe the second baseman gets the putout i.e. it does not affect his fielding percentage but the batter-runner doesn't get a hit. Reached Base on Umpire's Missed Call? Not sure how the umpire feels about, but the fielders sure know how they feel about it, and will let everybody in the stadium know.