DVD, as the Associated Press Stylebook points out only in its Internet guide, is short for digital video disk. But AP offers no guidance on whether DVD needs to be spelled out on first reference. Of course, it shouldn't be, in my opinion.
But if you look to the VCR entry for guidance, you'll find this outdated rule:
VCR Acceptable in second reference to videocassette recorder.Second reference?!
And one more quick comment: The DVD is the disk, equivalent to a videotape. The DVD player, equivalent to a VCR, allows you to watch the disk. Do not call the player a DVD, no matter what the teen workers at Best Buy say.