It sounds like there are two issues you experienced, neither having anything to do with the other.
I have no idea what the "rattling" would have been, but it certainly does not have anything to do with the stuck bullet. The cylinder falling off sounds like the yoke screw is very loose or missing. The yoke screw is the very front screw in the sideplate on the right side of the gun. The piece the cylinder rotates on and that retains the cylinder is called the yoke in a S&W.
Same for the small pin. It looks like about 1/2 of either the cylinder stop stud or the trigger stud or even the rebound slide stud. It would be really odd for any of these to break in the middle though, and virtually impossible for the piece to fall out of the gun without it being dis-assembled. Was this a new or used gun? Being a -6 it could be either. Either way, it sounds like the shop you are dealing with is first-rate and handling this in the best possible way. Even if a new gun, many dealers would just send it back under warrantee and let you wait for it. Did he have another in stock and make a direct exchange, or did he have to order one? If he didn't have another in stock that is something that couldn't be helped. If that is the case, then having it sent to the factory could be the quickest and best way to get you a functioning gun. S&W is just like most manufacturers in that sometimes quality control leaves something to be desired, and the gun could actually come back from warrantee as a better product than when it left the factory the first time.
Regardless of the wait, don't let this discourage you. S&W may not put out a perfect product, but they still make the best revolvers in the world. Their current production product is, in some ways, not as good as they used to make, but in others it is superior to what they made in the past.
Going back to the first problem, the stuck bullet. This isn't very common, but still not unusual. It has been known to happen with full power lead bullet factory .38 Spl. ammunition fired in a .38 revolver. It is more likely with jacketed bullets and longer barrels as above. To save money it would be far better to buy the equipment and learn to reload rather than buying the loss-leader ammunition sold by even the major manufacturers. Buy a manual, the Lyman Cast Bullet Handbook is excellent. Read it and learn as much as you can from it then come back and feel free to ask for suggestions on equipment to get into this at whatever level you would feel comfirtable at.
tomhaka,
Why did you delete you delete your post? I was in the middle of this and found it had been deleted when I posted it to save.