I've got an 850 that I bought off a friend of mine for a very good price.  The gun has less than 200 rounds through it.  The problem is that after any number of shots (10, 12, 20, no real pattern), there will be a very hard trigger pull.  Hard enough that you cannot squeeze the trigger.  You can relax from the trigger, it doesn't help.  If you rotate the cylinder to the next position, the gun will fire normally.  Go all the way around, and it will fire on the round that it jammed up on.  

If you dry fire, or pull the trigger with empty (already fired) cartridges in it, it doesn't do this.  It only seems like it's live rounds that this happens with. Doesn't matter if you're using a slow trigger pull, or a fast one.  Has anyone heard of this happening?  This is why my buddy sold the gun to me, as he got fed up with it.

ETA:  This problem is not specific to one ammo, either.  It did it with both Winchester and Remington FMJ rounds.

It really does sound like a problem with the hand or cylinder lock. Any play in the cylinder in the fired position?

There doesn't seem to be any play at all in the cylinder, at least that I can tell.

By it only doing it while firing live rounds it could be a clearance issue between the cylinder and frame, I have seen that in a couple revolvers before.

It has a lifetime warranty.   Give it a vacation to Florida and don't worry about it.

Holy crap, I just looked on Taurus's website, and apparently it does!  Thanks!!! I'll be giving them a call tomorrow.  

You are likely having case setback when firing a round which is locking up the cylinder/making it hard to rotate.

Clean and dry the chambers thoroughly before firing.

Sometimes, a weak/low power load makes it worse as the case doesn't expand enough to grip the cylinder walls.

If you stop trying to pull the trigger when this happens and immediately open the cylinder, does it drag more then it would normally?

It doesn't take much to cause a cylinder to drag and it can increase the trigger pull immensely due to how the rotation leverage is applied to the cylinder.