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?