PS3, Blu-Ray, and Samsung "Game Mode" Questions

[SDon1969]

Hello all! I'm new to the forum and recently upgraded myself to hi-def & blu-ray. The TV is a Samsung 40" LN-T4061F, and the Blu-Ray player is the PS3, hooked up via HDMI. When playing the XBOX 360 or PS3, the TV goes to "Game Mode" (it remembers to switch to game mode whenever the PC or HDMI2 inputs are selected). I don't really know what Game Mode is doing, the manual is vague and only mentions faster response times.

1) When I use the PS3 for watching a Blu-rays, should I be switching Game Mode off, or does it not really matter? I confess that I can't seem to tell the difference whether it is on or off.

2) The PS3 seems like a pretty decent Blu-ray player so far, any secrets to share out there? I did go into the settings and set the BD playback to 24 Hz as someone recommended to me. Are there any known issues with the PS3 and certain Blu-rays not playing, any incompatibility issues?

3) Sometimes I wonder if the TV is tuned as well as it could be - in fact, I'm sure it is not! Out of the box it had two setup options, Home or Store, so of course I selected Home to keep away from super-bright store settings. I do not have a trained eye when it comes to evaluating PQ, but sometimes I think I am seeing too much grain in some scenes and occasionally I see a "ghost" blob in dark scenes (Saw IV comes to mind, when Riggs is walking through his dark apartment with gun drawn, a ghost images appears on his face - my standard DVD does the same thing). I still have my old DVD Essentials calibration disc, should I try to use that on this new TV even though it is very old?