Every great mandolin player who gives advice on playing begins by emphasizing the importance of the right hand. I always read that, but either didn't pay attention or didn't know what to do about it. I finally wised up (a little), and I realized that I should work some every day on my right hand. So here are a few tips on working the all-important right hand. I hope other CoMandos will chip in with their tips!
Butch Baldassari recommends scales using all downstrokes. I was in one of his workshops, and his speed and precision are amazing! Try playing closed scales with all downstrokes, starting as low as possible and going all the way up the neck, with a metronome. As Butch says, whatever you can play with downstrokes, you can play twice as fast with down-up strokes. Plus you can really be a killer on those Bill Monroe stomp tunes.
Play down-up strokes without fingering the string with your left hand. Do this with a metronome, speeding up as you go. Start on the G-string, then the D , then the A, then the E. Then try alternating between G and D, then G and A, then G and E. Do this with all string combinations, up and down. By isolating just on your right hand, you'll have to pay attention to your strokes and attack. Plus the shifts between strings will be a great workout.
Playing scales, start with two notes per string, then play triplets, then 4, then 6, then 8, and so on. Do this as long as you can and you'll feel a real buildup.
Practice your right hand anytime you can, at odd moments. If you're resting and not really playing, work your right hand. I even do this while I'm reading my e-mail! Since I'm left handed (another reason I have to work especially hard on my right hand), I can scroll though e-mail with my mouse while I keep that right hand going.
This really is the most important aspect of mando picking. I hope others will add their ideas.