My dad showed this to us when we were kids, and I still laugh today. It's not a subtle or brilliant film, but it is full of great characters and comic performances from some wonderful actors, and it's got a good heart, too. It may be a bit old-fashioned, and the plot may not make much sense to the younger generations who can't remember the Cold War, but I'd recommend it as fun for the whole family. As a cold war satire it isn't as sharp or scathing as Dr. Strangelove, but for a family comedy it still manages to make it's point about the stupidity of the whole situation.
The DVD looks good--I originally saw it on VHS pan-and-scan, so to see the full picture is great, and the colour is sharp. The one small issue I took was with the subtitles translating the Russian into English (which you can't turn off). They weren't there when I originally watched it, and I'd be surprised if the original release had them, because they are rendered unnecessary by the acting. You can hardly fail to understand what is going on, with the gestures and facial expressions, and I found it funnier without. I think there was only one line I had originally missed that the subtitles filled in, and I found them distracting. Oh well, only a small issue with a good DVD.