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His staff did bad research. He had no idea who he was dealing with and the power Michael had.

Not frequenting a brothel would have also helped his position. Especially when he obviously made no attempt to know who owned the place, and made sure they kept his patronage discreet.

Did Rocco murder the prostitute while Geary was passed out in order to frame him and bring him under the Corleone's control? I got that sense from the shot of Rocco in the background of that scene and Tom emphasizing to Geary that the girl had no family and would not be missed and that the Corleone's would clean up the entire situation for the Senator.