I've flown to at least one match a year, since '01. I use a large duffle-type bag for my checked luggage. I put my range bag in the middle, then pack my clothes and other stuff around it. One time, I used my range bag as my carry-on, packing all my shooting gear in my checked bag, but then decided it was dumb to unpack the range bag for flying, then have to repack it for the match, etc., and post-9/11, I've decided the patches, pins, and that firing residue smell make it not so good, now.
One area where you will run into a lot of inconsistency, is the knowledge of individual airline employees. I've had some all but insist I unload and show clear, right at the counter, and others who don't really want to know what's in the gun case, as long as it's locked.
I've had people weigh my ammo, and others who don't even mention it.
I've heard some real good ones, like the counter worker who wanted the firing pin removed before she'd allow the gun to be re-packed. The shooter asked the gal if she'd know a firing pin if she saw it, and when the airline employee admitted she wouldn't, the shooter said, "Then let's not go there."
I had one of the TSA guys come to me, and with a completely straight face, say, "Sir, we found a dead animal in your bag." I'm sure I stood there looking surprised and confused, then the guy breaks into a grin, and says, "No, everything's fine." Later, my buddy suggested I should have said, "Was the fuse still in it?", but I'm sure the TSA guy wouldn't have seen the humor in that.