I picked up my first AR, a Bushy 20", earlier this summer.  I didn't get to shoot it much until the last two weekends.  Both of those weekends, however, I had 1 or 2 failures to fire because of weak primer strikes.  In every case, it happened on the first or second shot out of the magazine.  At the end of the shoots, I put the round back in the mags and they shot just fine.

I'm 90% sure the rounds that didn't fire were all .223s that I was just using up, and that the Q3131As and XM193s all shot flawlessly.  Still, and even though it's a new gun, this is bugging me.  Is this something I should worry about (well, I'm already worried).  I would appreciate any advice or suggestions.

And for what it's worth, I did strip and clean the rifle as far as Bushmaster recommends for "regular" cleaning before shooting it the first time and since then, with CLP.

Are you sure the bolt is locking up completely? It may be dragging over a full mag and not coming far enough forward to completely lock up.
It may just be a matter of wearing it in if it's a brand new rifle.

If you're sure you're getting a good solid lockup, I'd try taking the bolt apart and cleaning it again. Sometimes a little bit of crud will make the firing pin drag.
I had the same problem with my AR10 when it was new and I shot the harder military primers like the Port ammo has.