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So, I had an idea about what the Pirate Dispatch Society is.

Basically, my guess about how Buggy became shichibukai is A. He's a former Roger pirate. B. He was really flashy during the WB war. C. He posed a bit of a threat to the WG with his newfound crew, and D. He is close to and familiar with Luffy. The first 3 were obvious, but why the last one? Here's my idea-

Because Buggy is extremely familiar with Luffy's powers and history, as well as his former ally, this gives the WG, which is technically at war with the Straw Hats, an edge if Buggy were to become a shichibukai. On top of this, because he's a halfwit, he's easier to manipulate and control to their will. 

Now, as for the name "Pirate Dispatch Society". My guess is that the WG set Buggy to the task to finding Luffy and bringing him to justice, just because Luffy trusts him. Buggy, in turn, decides to gather up as many past-foes of Luffy as possible, ranging from Krieg to Kuro (basically any weak former enemy not seen during the 2 years later cover arc). So, basically, Crocodile and Daz would be the only ones who wouldn't be involved. 

Eh, the idea has some rough edges, and there'd be the problem with the point of reviving such old, weak characters, but if they were anything like Alvida, then they had the potential for a lot of change. 

I'd be glad to hear your own ideas and opinions.