I've often thought that Sol would have first approached Barzini first with his deal. Sol would have figured that Vito was already on top, with businesses that were a lot safer than drugs. But Barzini--younger than the other Dons, chafing to be Numero Uno, would have had the most to gain in a deal with Sol. Barzini would have told Sol that he still needed Vito's money and influence. "Go to Tattaglia--he's a pimp, Vito's worried about him. Tell Tatt anything, but I'll be your silent partner." If Vito said yes, Barzini would get silently rich on Vito's money and influence--and Vito wouldn't even know he was making his arch-rival richer and more powerful.

No high ranking Mafia guy ever carries a gun--too easy for any cop to arrest him for possession of a deadly weapon, just like a common criminal. Fredo was carrying that day because he had to bodyguard Vito in Paulie's absence--and for the dramatic effect when he fumbles the gun as the two guys shoot Vito.