The single most common mistake I have made, and that I have seen when tutoring others, is sloppiness. Especially losing track of a negative sign, either not noticing one in the original problem or forgetting it when writing out intermediate steps.
I find that most of the work where this is a problem is work that should be done with a computer algebra system. Those do produce a pretty dramatic reduction in error rate.
I'm mostly asking this open question to those among us who are well-versed in developmental psychology (I'm mostly thinking of children) . Although, failing the actual scientific research on the topic, I guess some testable hypotheses would be great too.