I want to describe the problem I've had and how I solved it in case somebody else has the same problem. (If so, please reply to this thread in order to show how often this problem occurs...)
I downloaded, installed, started, played. (On a MacBook Pro with 10.5.8.)
It was great fun and to let the game also look pretty I've set the resolution (in full screen) to 1440x900 which is the native resolution of my display.
After I finished playing the intro, quite at the beginning of the credits (after I saw Sam & Max driving in their car) the game stopped while showing S&M on artistic background. It then crashed and when I restarted the game I had to start from the beginning.
I played the intro a second time using a different, lower resolution this time and had exactly the same problem.
Then I did three things: I have copied the game again from the .dmg to my Applications folder, I've changed the resolution to 800x600 and turned of full screen mode.
This it it worked. I don't know if copying the game again or changing the resolution/ screen-mode solved the problem, but I am tired of playing the intro and will not try that out... ;)
Hope this short report helps somebody!