How to tell if a DVD is enhanced for 16:9 mode
As detailed above, a DVD that has been made by an anamorphic transfer (aka an 'enhanced for 16:9 DVD' or just 'an anamorphic DVD') will have higher picture quality.
However, it can be hard to tell from the cover if a particular disc is anamorphic. It's not uncommon for the cover information to be missing, misleading, or even flat out wrong.
Here's how to test if a disc is anamorphic:
Set your DVD player to '16:9 Television' mode.
Set your television to 4:3 mode. (If you have an ordinary television, this is the normal mode. If you have a widescreen television, 4:3 mode is the one with big vertical black bars down the sides. Either way, make sure you're not in any kind of 'automatic' mode - you want to force it to stay in 4:3.)
Play the DVD.
Observe the results. If the picture is vertically distorted, making everything appear unnaturally tall and thin, then the disc is anamorphic. If the picture is not distorted, the disc is non-anamorphic.