It appears that some people have been experiencing overheating issues, but for me playing on a Xbox360 S console does not offer any problems so far. I am now in my third disc of L.A. Noire.
[Update]: For some reason, my other Xbox360 console, a first-generation from the year of launch (2006) seems to be having problems with loading the game. I have contacted Xbox Customer Support this morning (20 May) and will update the outcome accordingly.
[Update]: I was informed by Xbox Customer support that an automatic update when connected to Xbox LIVE should resolve the issue.
[Update]: At 9.00pm (20 May) Singapore time, there was no update initiated when I launched L.A. Noire from the first-generation Xbox360 console. While the console has no problem launching other games, it still freezes at the opening screen.
[Update]: At 10.00am (21 May) Singapore time, I launched L.A. Noire from the first-generation console and to my surprise, it loads fine – without any auto update. Ran through the opening cinematic up to the gameplay scene, before I decided to quit the game. Was it due to insufficient memory? I rechecked the existing consumed memory and removed an additional 1.1GB worth of old games’ files. Hopefully, there are no more problems. There was no problems playing the PS3 version other than the inability to access downloadable content as the PlayStation Network is undergoing maintenance.
[Update]: At 11.00am (22 May) Singapore time, I launched L.A. Noire and there was an automatic update for the game from Xbox LIVE. According to PlanetXbox360, it does a few things.