The two most important aspects of shooting from the helicopter are standardized communications between the aircrew/sniper and a good stable shooting platform. Standardized comms between flight crews have been the norm for years and any good helo sniper training program will ensure that snipers learn these standard DoD communications procedures. This ensures smooth communication when the sniper takes control of the scene, provides airborne support or needs to maneuver the helicopter into position quickly. A stable shooting platform is achieved by using a specialized sling system that can be quickly rigged up by the sniper and attached to hard points on the helo itself. Using this system, I've personally taken live shots up to 300 yards with 1 Minute of Angle (MOA) accuracy.
Before taking over the SEAL Sniper training program as Course Manager I taught advanced helicopter sniper operations at the Naval Special Warfare TRADET Sniper Cell. While I will not go into exact training techniques, I can tell you that we had an excellent helo sniper training program (my good friend Eric Davis and I re-wrote it). We put our guys into live helo's with live fire, moving targets and complex scenarios to include vehicle interdiction and ship take-downs.
Jack is right about the uselessness of using scoped weapons out of the helo, it's a fools game. Red dot or laser is the only way to go. Shooting someone? Take a semi-auto (.308 or 5.56...I'll take a .308 thanks). Taking out an engine block be sure to use a .50 cal or .338 bolt action.
While attached to SEAL TEAM THREE pre 9-11 I was fortunate enough to log many hours supporting hostile ship take downs as an airborne sniper supporting the UN sanctions against Iraq. We would typically take down 1-3 ships per night, often times our boarding teams would have cut their way inside the ship with a torch. I've also been fortunate enough to have a few vehicle interdiction Op's in using the .50 cal. All good stuff.
Bottom line is that Helo sniping in our community is something we practice on a regular basis and is here to stay. The situational awareness (squirters, hook points, active shooters, etc.) that an airborne sniper can provide to a team leader is priceless.
Look for a helo sniper excerpt from my memoir titled The Red Circle (St. Martin's Press 2012 release) in the next week or so.