I remember showing a coworker a complexity analysis I did, where I'd written "0.002 n lg n + 3n". I was surprised when they asked "why did you put the insignificant one first?" but then realized... that's exactly right! Even for universe sized problems, 3n is more than 0.002 n lg n.

Basically, as soon as you care enough about constant factors to actually compute them, some of your habits from doing asymptotic analysis can be actively harmful.