Respectfully, I don't agree with your take.

Michael did keep Fredo close, as close as was possible for someone of Fredo's...simplicity. All he could be trusted with was the 'picking up someone at the airport' or planning the parties or running the brothels.

In fact, it had been Sonny, years earlier, who had sent Fredo away to Vegas, when he suffered a breakdown after proving incapable of even attempting to defend his father from being gunned down. Fredo never returned to New York. Michael went to Vegas and kept Fredo under his wing, took care of him, gave him the only kind of work he could handle.

Michael had no reason to distrust Fredo or keep him under a 'watchful eye', prior to the hit attempt by Roth. Because Fredo kept his resentment to himself until Johnny Ola came along to stir it up.

There was nothing 'sloppy' about the way Michael handled his brother. Either before the betrayal or after. And use all the psychology you like, but the only thing Michael intended to 'erase' with Fredo's killing...was Fredo, and the risk of another betrayal somewhere down the line.

So...back to the original thought...what WAS Michael's weakness????

AppleOnYa