My Browning BDM that I have been so pleased with up until this point exhibited some failures to fire today.  It would, however, fire the round with a second hammer blow each time.  All of the various brands of ammunition I tried seemed to exhibit the same oddly offset primer hit.

I am thinking the firing pin is slightly bent, although I have no idea how that happens.  It seems to be bent so it sets off most rounds but a few are just far out to not be hit hard enough for ignition on some.  All other functions like ejection are fine, and there is no pattern to this malfunction.  My thought would be to replace both the firing pin and spring while I'm in there -

Do you think this is the correct diagnosis and cure?

Nope, a bent firing pin would not do this on any semi-auto because the tip is guided by the firing pin hole in the slide.

Its more likely that the gun is trying to fire with the slide SLIGHTLY out of battery; the breech end of the barrel tips up into the slide as the gun locks up (cycle it by hand to see what I mean), so if slightly out of battery, the firing pin will not align fully with the primer.

My first guess would be  oversize ammo - are you running reloads or factory? Could also just need a good clean, or something might be defective (e.g. weak recoil spring). I suggest you give it a good clean, including around the barrel hood and locking lugs, get some new factory ammo, and see if the problem works itself out.

All good points, but the ammunition mentioned was all factory stuff.

My statement stands - the most likely cause it that the gun is trying to fire from slightly out of battery. You need to find out why - this is a safety issue, not just a reliability issue.

I agree with the above post. An OOB discharge will be very unpleasant and possibly very dangerous. You might start with a thorough cleaning and lubrication if the gun is extremely dirty. I would also replace the recoil spring if the gun has been shot very much or is old.

34,000 PSI gas will just toughen up his face a little.

It is the brass shards that are the problem.

This.

Probably need a stronger recoil spring.  But dirt or other debris, or weak ammo, might slow feeding enough to cause this.  It is potentially a dangerous situation.  Identify and correct the problem before continuing to shoot the gun.They probably fire on the second strike as the first hammer fall drove the slide into battery.

I would take it to a good pistolsmith to check all of the above, together with the timing. Could be time for a new barrel lug link and pins.