The minefield at the bottom of the first hill was marked at the beginning of the scenario (or shortly thereafter -- I forget). I got some engineers down to the scattered trees near the minefield where they sat a few turns. Voila, the sign went away.
Quite a while later, after knocking out the Panther, I sent a Sherman merrily down that road and BOOM, it got knocked out by the minefield. Suddenly the mine sign was back up. Doh!
Questions: How close do the engineers have to be to disable the things? Why did the sign disappear and then reappear only after I was suckered into driving over them? Hopefully this is covered in the manual in greater detail.