Once your form falters, you STOP, take a deep breath and continue at a slower pace correcting the faults in your form. Sloppy reps do not count. Improper form also makes lifts more difficult which always encouraged me to go slower and maintain form. Being hasty and forgoing a second or two for necessary rest also makes failing a rep more likely, which wastes the most time. And Greg Glassman said it himself, "You go faster and faster and faster until you make a mistake, then you slow down and stop making the mistake." You do not make a mistake and tell yourself, "Oh well. It's CrossFit! It ain't about form. It's about reps, baby!" That is incorrect.
Also, AMRAPs are endurance workouts. You're supposed to maintain an above-average pace for an extended period of time. The reps are low to moderate (think 15) and the movements compliment one another; the time performing one movement allows you to rest from the previous. A 5 minute AMRAP would not train you to endure anything other than arithmetic.
I have been Crossfitting for five years and have lung capacity I thought was not possible. You'll hit a point where you are practically never out of breath; burpees will hit your legs before your lungs. Bodyweight stuff is a joke, and such focus on form carries over to heavy lifting. I always felt emphasis on bodyweight movements reinforced my weightlifting form because I was aware of my body's movement and knew what felt comfortable and powerful and what felt uncomfortable. It's easy to get pulled into the attitude of Crossfit. Hell, that's all the site has been selling since 2010 (take a look at their t-shirts). Do not swoon over the marketing junk. Look at the Crossfit Games athletes - the most perfect form throughout the hardest WODs. I never admired the fools rolling on the floor gasping for breath; I watched Chris Spealler rip through long workouts without ever stopping to rest and finishing standing, walking around like he was not phased.
I love their slogan, "Yesterday you said, 'Tomorrow.'" I have gotten a surprising amount of motivation out of goofy slogans.