Sonny probably never let the thought of a set up enter his mind after he got a call from Connie. His temper took over all normal thought process and all he had on his mind was taking care of Carlo. It was more anger clouding Sonny's thinking than anything else. If he hadn't been hot tempered, he may have seen the set-up all along, had the novel allowed it.
Barzini knew Sonny would be a threat but never thought that Mike would be because up to the point where Mike comes back from Sicily, he's not involved in the business. Only Sonny and Fredo - " well to a point where Vito let him be involved because Fredo, well Fredo you know."
Mike probably knew that Vito did not want Carlo involved in the family business, I know its not in the movie, but like some of the plot dead spots we assume that certain things were filled in due to the movie progression. Mike knew at the meeting where we first see Neri as Mike's enforcer. When Tessio and Clemenza asking for their own families, when Mike told Carlo that Carlo would be his right hand man in Vegas, he already had Carlo lined up to get whacked. He was setting Carlo up, he already had his demise set up, just had to pick the right time.
He was still waiting to see who else would betray him. As Tom asked Mike right before this scene ended, Tom asked Mike - Why am I out, why does Neri report directly to you, he asks about Rocco building a secret regime. Mike asks him how he knows this. Tom says that some of his men are to good for their job, that they are getting more than the jobs worth.
Keep in mind, this is the first scene after Mike talks to Kay and Mike tells Kay that he has been back for more than a year. So there in theory, there is a year missing from the movie that Mike has been in charge of the family and been plotting and planning making decisions.
Mike had to let the pieces fall into place between this point and the move to Nevada. I believe then and I belive that now that Mike knew Clemenza would not betray the family.