This might sound like a stupid question but how does the DVD drive in a mac mini compare to a regular DVD player? If I hook it up to a TV, how will the picture quality be? Can it replace my DVD player?
The Mac mini does have S-Video and composite video output with an optional cable you'll have to pick up separately. It makes an adequate DVD player and a Mac mini could allow you to quite happily get rid of your DVD player. It's not a home-theater quality player, but I doubt that is what you're after anyway.
Not that many TV sets have DVI-ports, ApeintheShell... But yes: Digital inputs are preferred. But basically, the picture will be good if it's HDMI, DVI, VGA. Less good with Composite, S-VHS etc.