In G1, in the scene in front of the hospital, when Michael takes the lighter from the baker's
trembling hands and lights his cigarette, he
holds the lighter and seems to study it intently.
Did I miss something?

The whole hospital scene shows michael's coolness and quick alertness to emergency in protecting his father.

Once the car full of solozzo hitmen had left, enzo the baker was seen as shaking and nervous as to what had jus happened. When enzo tried lighting his cigarette he could not due to his shaking. Once michael held the lighter he noticed that his hands were perfectly still and he was not shaken to bits like enzo was.

This was the realisation that he had become sort of like his father calm and cool in emergency.

Many see this scene as the defining moment of michaels transformation from a 'college' boy to the don we see later on in the trilogy.

wow I never even thought of that as par tof transformation into a Don. Interesting, maybe I'll have to see this scene now and look at it differently.

As I have posted before about this scene, that was the defining moment for Michael. He and Enzo face death when those cars pull up, and after they pull away Enzo, understandably is shaking uncontrolably. Mike takes the lighter and calmly lights Enzo's cigarette, and as you said looks long and hard at what he is calmly doing. I think at the very moment Michael realized that he could live this "life" without any problem. That he was a natural at it. I think that many things ran through his mind at that split moment. He also realized that had he not been there to stand outside and act like a bodyguard, his father would have been killed in that hospital. Mike, thinking all this knew that he now must get involved in order to save both his father's life and the family itself.

Don Cardi

wow, that never even occured to me. great views. i mustve read too deep into it; i was thinking that it was almost a click in his head that the cops and sollozzo were connected. as soon as the men left in the car mike and enzo start relaxing then he hears sirens.......click........the cops come to escort mike off the property, funny coincidence.

click

i totally got the same opinion like don cardi, as i watched the scene i just thought that michael realized in this moment he lights the cigarette that he wasnt scared and that he could get into this business. i also think thats one of the things that changed his mind, "thats my family, not me" he realized its him 2.

Michael's intention outside the hospital was just fabulous.

I think the reason why Vito made it thru the 5shots was because he knew Sonny and Fredo couldnt be good Don's at that time of Sollozzo and Tataglia

Mike is also in a way used to this tension, due to his expeirience as a soilder in WWII

I used to think that there was something about the lighter itself that caught Mike's attention. However, the novel specifically states that Mike was surprised that his hands were steady.

This is a scene where FFC really deserves some credit. This was a major turning point for Mike. The only line from the book is this,

"To his surprise his own hands were steady".

FFC really managed to demonstrate this as THE turning point for Mike, a point at which he trasforms before our very eyes. I think this scene rivals the "I'm with you now Pop" scene in the hospital in showing Mike's transition.

I agree about those two scenes; I get goosebumps every time I watch them. What amazing attention to detail, on FFC's part.

also you can assume he faced worst situations on his life during the war