My Mac Mini will read some commercial DVDs but not others.

I have a Mac Mini running Snow Leopard 10.6.8 on a 2.53 GHz Intel Core 2 Duo processor. I've had it for a couple of years now and just recently decided to run one of the video ports out to a wall mounted LCD TV for viewing both internet tv and DVDs. However, turns out my DVD player (SuperDrive, and rarely ever used ... maybe 10x since I bought the thing) won't read certain DVDs. For instance, it will mount and play Charlie Brown's Christmas, but not Pirates of the Caribbean. It appears to be a 'new dvd' vs 'old dvd' issue. Is that a real issue? Is there software I can install that would cause the drive to mount and play my newer DVDs? I'd appreciate any advice here. Thanks.