*sigh* He shouldn't have entered in to a field of knowledge of which I am quite familiar:
Jones' claim after the first round: 100 bb's in the load, 50 hit the target
fact: there are ~345 7 1/2 size pellets in 1 oz of shot. This means that there are ~258 pellets in 3/4 of an oz of 7 1/2 shot.
http://www.shotgunworld.com/amm.html
Looking here
http://www.angelfire.com/tx/ShotGun/ , under the Pattern section you can see that for cylindar (no choke, which was Jones' first shot) you can expect to retain 25-35% of the shot within the kill circle at 40 yards. This equates to 64-90 pellets hitting the target. 40 yards is further out than Cheney was, iirc. I believe Cheney was at ~30 yrds.
2nd round: if this is truly using the "modified" level of choke, we can expect 45-55% of shot to be within the 30" circle at 40 yards. This comes out to 116-141 pellets.
I'm not even going to comment on the "soft rubber" kickboxing dummy, beyond saying that the claim that its material is "very similar to human skin" is crap.
Per
http://www.winchester.com/products/catalog/shotdetail.aspx?symbol=X28H7&bn=1&use=6, we also see that (and this is just a standard load, I do not know if Cheney was using hand-loads or not) a 2 3/4" 28ga 3/4 oz shot shell will have ~1205 fps at the muzzle.
Jones' pattern complaint. He's wrong. Consider
Good to 35 Yards. It surprises many shooters that the 28-gauge delivers a consistent pattern out to 35 yards. On a percentage basis, the 28-gauge will put as much of its pattern into a 30-inch circle at 35 yards as a 12- or 20-gauge will. This makes the 28-gauge ideal for small-game hunting within that distance.
http://www.progressivefarmer.com/farmer/outdoor/article/0,24672,1112682,00.html
http://www.angelfire.com/tx/ShotGun/ Pattern section as mentioned above
http://www.shotgunworld.com/amm.html
Typical Shot Spread Per Choke
Choke....Yards
.........10.....15......20......25......30......35......40......45......50
Full.....10"....15".....20".....25".....30".....35".....40".....45".....50"
Mod......15"....20".....25".....30".....35".....40".....45".....50"
I/C......20"....25".....30".....35".....40".....45".....50"
Cylinder.25"....30".....35".....40".....45".....50"
Dummy, chicken & watermelon: Jones never clarifies which choked barrel he is using. He could well be using the cylindar choke, which has a much larger spread than the modified choke.
Additionally, it is clearly windy. 7 1/2 size shot is only .095" in diameter, and is quite vulnerable to wind drift. This will affect the patterns observed upon the target.