Almost any heruistic can be "most harmful" if used by a teacher in a situation when the audience does not know why it makes sense, and without an explanation. This is especially dangerous in the frequent case that the heruistic does not actually seem reasonable to a person seeing it for the first time, since it makes sense only in some ways but not others. It might require months of experience for an uninitiated person to understand how and why it applies.

For example, the heuristic of schemes as manifolds is such -- every algebraic geometer understands it, but it actually is harmful to a person who is seeing schemes for a first time (such a person would vary likely interpret this heruistic as saying that affine schemes are trivial to understand). Same applies to "integration is the inverse of differentiation", and some of the other answers to this question.

Of course, these heuristics are also the most useful ones, once you (and any audience you might have) actually understand them. The whole point of learning math is to gain more such heuristics, and to makes the ones you have more precise. For this reason, it seems to me that the use of such heruistics on an unprepared audience is the most common problem in the lectures by the very best mathematicians.

A related problem is the an abundance of statements that are not strictly true, but "correct in spirit". Again, this may be very useful in research or when talking to a person of appropriate sophistication, but it is very bad for students if such statements are used carelessly and without explanation.

P.S. This whole answer is generalization for the sake of generalization. Was it a waste of time, I wonder?