As Clemenza gives Michael shooting instruction, he jams a hat down on Michael's head and says, "It helps against identification, just in case. Mostly, it gives witnesses an excuse to change their identification when we make them see the light."

Anyone think Solozzo wouldn't be suspicious of Michael sitting there eating veal with his hat on?

Nah. Dressy hats (like fedoras) were so much the norm back then, I really doubt it.

...or, Michael would put on the hat as he was leaving. Since no one would have paid much attention to him before the shooting, they'd look up--and see a guy with a hat. That'd add to the variables that witnesses might offer the cops. Clem had a good idea.

BTW: when Gotti had Castellano whacked, all six gunmen dressed in identical hats and coats, and used identical weapons. That made it next-to-impossible for witnesses to positively identify any individual. None of them was ever indicted for that murder.

An interesting tidbit. According to Gangland by Howard Blum, 5 of the 6 hitmen were wearing identical outfits. Fat Ange Ruggierio was in charge of finding the hats and coats. One was a yellowish color, while the others were all an off-white. This deviation drew the wrath of Gotti before the shooting. "Yellow! Mother f--kin' yellow! Are you kiddin' me?" was what he reportedly bellowed at Fat Ange. After a tirade, Gotti calmed down and said "What the hell. It'll have to do."

Sammy the Bull, one of the conspriators in the plan to whack Big Paul, was unaware of the plan to have the similar outfits of the shooters. He was struck by Gotti's cleverness and had more confidence in the plan as a result.

Did anyone notice though if Mike picked up his hat on the way out? I don't think he did.

In the movie, Mike picks up his coat on the way out. Can't really see the hat, but it could easily be under the coat. He doesn't put it on when he gets to the street.

I think Puzo picked up some hat lore and put it in Clemenza's mouth, and then just forgot that it really wouldn't work if Mike was sitting down to dinner with an experienced gangster.