3. Using such pistols to shoot at a human silhouette at an estimated 25 yards and not being able to stay on paper. Heck, shooting so far off the mark it goes off-bore 5+ feet at an estimated distance of 25 yards.
Pretty awful gun stuff.
Bonus Goof:
Murderer "modified his father's [modern] shotgun to fire lead balls."
If they were smoothbore, with balls, I gave them poetic license for #3. Granted, it's not so bad that someone could not hit another at 40 paces that it fails as a "technical" plot-point, but there's no good way to demonstrate the more subtle inaccuracy of smoothbore muskets and balls, over rifled conical bullets in a TV show.
Something with at least a kernel of truth to it usually gets a pass from me in a fiction setting.
Same for the bonus goof.
Prying open the crimp on a cheap birdshot shell, dumping the shot, and stuffing something else in there like an antique lead musket ball, then firing it is somewhat plausible. Although they flubbed the line by saying "modified his father's shotgun to fire lead balls". They should have said, "cut open a modern shotgun shell, dumped the shot, and put the lead ball in there..." and the audience still would have gotten it.
Honestly the "Blackpowder social network of New York City" was the unbelievable part. Although at least they knew they had to put some kind of McGuffin in there because BP stuff isn't nearly as regulated as modern firearms. (OTOH, they may be in NYC, shrug...)
And uh.. she's only seventeen (I think) and if I were to comment on the actress that plays Nathon Fillion's daughter on the show, I might get a visit from Chris Hansen... er... so I won't.
And I preemptively point an accusatory finger at ANYONE who's ever said one word, or ever had so much as a stray thought about Summer Glau when Firefly was still on the air. (Hmmpf)