The advising student pointed out that many of his "silly mistakes" were likely due to his lack of true mastery of the mathematical concepts as well as lack of facility with solving complex problems. He pointed out that he himself rarely make silly mistakes on the AMC10 and AMC12, but that he used to make lots of them a couple of years back when he was merely familiar with these same concepts and relatively inexperienced in solving complex problems.
I definitely am considering this possibility as well. The interesting thing is that DD is one of those kids who learned her "facts" instantly and effortlessly, and was always strong with computation. However, I do see that sometimes she doesn't see the forest for the trees and misses things that should have let her know her answers were wrong. I like the emphasis they put these days on "Is my answer sensible?" but DD often doesn't seem to see that stuff. It concerns me in that I sometimes feel she is a little "math robot" without as much deeper understanding. I still feel confused about her true math aptitude all the time--she has flashes of real strength but other times I see surprisingly weak skills.
ETA: Like a poster above, she also will rely too much on doing things in her head and suffer for it. She dislikes "writing too much down." This is probably classic giftie.
