If I had a penny for every time I see a player forget to take advantage of movement strategies, I would be a rich man...
The error that I see most often in tournament as well as casual play is negligence with moving active units. Whether it is simply moving a character to gain height advantage, moving ranged units back to avoid immediate melee counter attacks, or moving around an engaged unit (maintaining engagement) to better control travel lanes of the enemy, players seem to forget that just because their unit is within range of an enemy unit doesn't mean they need to forgo their movement phase.
Melee Dance... back in the early days of Heroscape I think I remember a description of a melee engagement occurring up a hill as a "do-se-do". One unit would attack and then the other player would move his unit around to gain height and attack, and so on and...