So, under Eliezer's suggested criterion (turning true to false) this is not a flawed step, though if you look carefully enough, you can still notice the flaw - a division by zero.

Hmm. A failure to identify a flawed step doesn't mean that the step isn't flawed.

A true statement turning into a false one does show that you manipulated it badly - but a true statement staying true doesn't show that you manipulated it well.