Yeah, Joe, you got it. The original script had Bailey as a senator, but that was too high a profile for the purposes of the plot. Making him a secretary was better, but not perfect: it's still a presidential cabinet position, subject to congressional approval, and therefore, subject to a certain amount of publicity. Maybe Noodles wouldn't have noticed, but someone else surely would have, and they would have raised a stink, then it would have become a news item, and then everyone would know.
And why would Max, anticipating these very problems, allow himself to be put forward for confirmation in the first place? Why not have a mouthpiece operating as the secretary through whom Max could work? The one law that every old gangster knows is, Stay in the Background. Max's failure to follow this is a flaw in the logic of the plot.
Either way, this gets noticed, until finally scandal attaches.
Except that he somehow got through the confirmation process without anyone finding out about his past. Certainly he would have been found out once in office, but I don't see how he could have avoided scandal even as a nominee. Red flags would have gone up from the get-go, he would not have been confirmed, he would have been asked to withdraw his nomination, etc. But somehow he became "Secretary" Bailey. It's not credible. I blame SL's lack of familiarity with the U.S. political process.
It looks like credible to Europeans. At least I'm buying it, and noodles_leone seems to be buying it too. Okay, maybe now when you have pointed out some things I'm having second thoughts. But honestly I never had a problem with Max becoming Secretary. Leone said something like: "OUATIA is America seen through European eyes". And European eyes are much colored by movies.
Are you saying that from a European point of view, everything can happen in America? (Both good and bad things.)
Not everything. But you know, everything's in bigger scale there.