In all honesty though, pivoting/DA dash can be somewhat useful for Mario. It's certainly helpful when you're extremely close to the opponent and out of sweetspotted f-smash range. . .in that case, you can dash away into a pivoted + sweetspotted f-smash. It's much faster than wavedashing back -> f-smash. Combining pivoting with f-tilt is also pretty useful, since you can back away and f-tilt without fear of being shieldgrabbed if you happen to be too close.
As for what Mario players need to learn, you certainly need to know how to combo, since Mario is, in fact, a combo centric character. Getting familiar with your opponent's weight/falling speed, and especially following DI plays a major role in how many consecutive hits you'll land. Learning to techchase helps extend combos, as well.
Landing and incorporating grabs is also pretty important. Yes, Mario has a fairly decent vertical launcher with his u-tilt, but most of his combos stem from grabs. Once you grab, you have a whole gamut of opportunities at your disposal--u-air chains, chaingrabbing, u-tilt/u-smash alternating, etc. And learning when and how to grab is extremely hard, given that Mario's grab range sucks, and that practically everyone outranges/outspeeds Mario (think Fox's shine, CF's n-air, Marth's sword, Peach's priority).
Those really make Mario what he is. A Mario that doesn't grab is crap. A Mario that can't combo off of grabs is crap. Not to say that the player is bad, but they're simply not maximizing the character's potential.
Other than that, certain things come to mind--learning how/when to KO is important (Mario's KO inability), as well as edgeguarding (since edgeguarding basically replaces outright KOs).
But learning how to consistently land grabs, and combo/follow DI is by far one of the more important things to learn with Mario.
