If you think about it, the term “the mob” doesn’t really make sense in reference to organized crime. A criminal organization is by definition the opposite of a mob; it’s a small elite group, as opposed to a large crowd of common people which is what “mob” literally means. So how did the term come to mean what it now does?
I asked a similar question once that got some good responses. I was going to say that it was a while ago but it looks like it was a really long time ago. It doesn’t directly answer your question but it should help.
“What is the difference between “The Mob” and the Mafia?”
http://boards.straightdope.com/sdmb/showthread.php?t=55674&highlight=mafia
Here, the ‘mob’ always meant the Army.
It’s a natural progression from the original sense of the word mob.
Initially mob was a contraction of the Latin phrase mobile vulgus, the fickle crowd. First cite for this in OED is 1688, under the definition ‘a disorderly or riotous crowd, a rabble’.
Clearly it’s not a large jump in sense to apply the term to a rabble of criminals, and this specific sense has an earliest cite of 1826 in OED.
A century later we find it being used in the originally American sense of a gang of organized criminals.
etymonline.com says 1839 in Australia, 1927 in US.