Did the Mob world respect Mike when Vito transferred power to him overnight? Or everybody thought he was a joke until he started to whack his rivals one by one and made his prescence felt?

I wouldn't go as far to say that he was regarded as a "joke" -- certainly everyone knew he was responsible for killing Sollozzo and McCluskey -- but he wasn't held in the same high regard that his father was, either.

Even within his own inner circle there were doubts. Clemenza begged to start his own family, and Tessio, of course, ultimately proved to be a complete traitor.

But after he killed everyone off, I would imagine it was a different story.

i'd think that if vito made a decision, the other families wouldn't need to hold a respect. vito says micheal is the new don, then so be it. of course they all looked at micheal as if he was still a child, but all the same, vito trusts micheal with the family, then thats all they should need to know and understand.

The novel says that the general view of Michael was that he wasn't the man his father was. Even Tessio and Clemenza, while giving Michael credit for a "bravura performance with the Turk and McCluskey," thought he "lacked force." Of course, that's exactly what Michael wanted: for both friends and enemies to underestimate him, the better to test loyalties and expose weaknesses. After the Great Massacre of 1955, the survivors had a different view of him.

It's said in the book that one of the many things Michael learned from his father was to have your enemies overestimate your faults, and your friends and family underestimate your virtues. Michael pulled it off in spades, and everything came full circle during the baptism scene. By Part II, Michael was presumably the most ruthless mob boss in the history of the American Mafia, wiping out nearly all of his enemies. The scene in the boathouse, where Tom tells Mike it's impossible to kill Roth, it reminds me of the scene in Vito's study, where Sonny and the caporegimes are making the "hit-list." Tom says something to the effect of "The key is Sollozo, you take him out, everything falls into line." Sonny wanted to hear nothing of it. In the boathouse scene, Tom asks Michael "You've won, do you have to take everybody out?" Mike says "I don't feel I have to take everybody out, just my enemies." To sum it up, I don't think Mike even sought the respect of the rival Dons, seeing as he took them all out. He didn't seek respect from any of his enemies, he let his actions speak louder than words.

Yeah you're right. He basically just does what he feels is right based on the info he has (killing anyone who needs to be killed in his wake), and respect or opinions is irrelivant to him. However, the others probably didn't think much of him before all the hits, considering that he was the youngest Don in the country (at the meeting according to the book Falcone and Molinari are).

I think there was a big difference between Michael and Vito. Michael had more of a temper (Vito would never raise his voice to Tom Hagen) and he was less reluctant to settle things through negotiations. In the scene where Vito makes the deal with the other families so Michael can come home, he makes the point that he has "never" refused an accomodation except on the drug issue. Michael, on the other hand was never interested in accomodating anyone.

No question that everyone feared Mike, but whether they respected him was something else. In GF III even Don Altobello, an old ally devided it was time to take Michale out, and Michael himself in the famous Dontomassino open casket speech asks out loud why was Dontomassino so loved while Michael was so feared even though both of them were equally honorable.
Michael was not loved because he didnt give much. Vito built his empire on doing favors for other people and then getting favors in return. Michael did it more form the barrel of a gun.