There are a lot of people who still haven't played many games of 8th Edition, and are assuming things play the same as before... and are playing wrong. Take some time and read the entire book, and then read it again. After reading Jervis Johnson's article on the Games Workshop website about some of the Easy to Miss Rules, here are my thoughts on his points.
Templates: Everything is hit. No more partials. But if an old army book still lists partials as being 4+ to hit, you have to play with the old army book rules! I am going to have to dig through some old army books so I know who these armies are.
Sequence of play: This was something Brian of the GLWL brought up on their forums, that I made use of in our game at 3000 points. Charges are declared one at a time. Charge reactions are carried out immediately! Before the next charge is declared even. If you then charge a unit who is already fleeing, it flees again automatically. I made use of this in my game vs Lizardmen and had a unit of Saurus fleeing from my table edge all the way to his table edge in a single turn, allowing me to score points for the unit the next (and last) turn when they ran off the table. Also, charge moves are carried out after all reaction, but before the compulsory movement phase. This is different than last edition.
Pursuing and Fleeing: units with the Swiftstride rule (mostly cavalry) roll 3d6 and take the highest 2 dice totals.Flying units flee and pursue on the ground! This means they will not flee 20" anymore. And finally, models with random movement always move their random movement. Yes, my Doomwheel and Hell Pit Abomination do flee and pursue 3d6 inches TOTAL.
Magic: If a wizard fails to cast, his magic phase is over. Be sure you don't throw 2 dice at a low level spell first thing, you may always roll 2 or 3 and be done. The same with dispelling. You may still dispel after failing, but not with that wizard... losing his magic level bonus to your dispel roll.
Reforming: A unit can get specific situation reforms if it destroys an opponent and does not overrun, or passes a leadership test to not pursue a fleeing unit, or it destroys a fleeing unit and passes a leadership test, or is the loser in combat and passes a leadership test. That final version of combat reform applies the combat modifiers you lost by! Steadfast also applies. Swift reforms are a thing of greatness. If you have a musician, you can take a leadership test in the movement phase to reform and then move regularly, without marching. If you fail you may only reform.
Panic Tests: are taken immediately after they are triggered. But only one test is taken per phase.
Flaming attacks: cause fear in war-beasts, cavalry, and chariots, and allow you to re-roll to wound vs units inside of buildings.
These are some of the interesting ones that have come up again and again vs new 8th Edition players. The rest of Jervis' article is a good read if you aren't completely familiar with 8th Edition yet.
Any other rules you have missed in 8th Edition, only to later find out you've been playing them wrong?