TB, I have to side with Pete on this. I've never found anything suspicious in Mike's expression when he mentions Ola and Roth to Fredo. I don't see it. Plus, how many people could Mike have known in Cuba the names of which he could have mentioned to Fredo?

As far as Vito's association with Roth goes, as the book states, in the early 30s Fredo was still in high school. We only know of Vito's association with Roth from the films, not the book. Even so, from the novel's limited reference to years, we can infer that the association with Roth takes place when Vito's kids were quite young and I also doubt that Roth was ever around Vito and his family for the kids to know and remember who Roth was in the same way as they were around Clemenza. They are two totally different associations. Again, as the novel states, even Sonny at 16 or so went to work for Vito, but only after Sonny requested doing so and then was used in a cursory manner throguh Clemenza.