The three Godfather films have been restored, remastered, retouched, unscratched, and cleaned for release on Blu-ray and DVD.
By all accounts, the original negatives of the first two films were so torn up and dirty that they could no longer be run through standard film laboratory printing equipment, and so the only option became a digital, rather than a photochemical, restoration.
The final product, which the studio is calling "The Godfather: The Coppola Restoration," combines bits and pieces of film recovered from innumerable sources, scanned at high resolution and then retouched frame by frame to remove dirt and scratches. The color was brought back to its original values by comparing it with first-generation release prints and by extensive consultation with Gordon Willis, who shot all three films, and Allen Daviau, a cinematographer ("E.T.") who is also a leading historian of photographic technology.
The article goes on to say that the Blu-ray version is like a "pristine 35-millimeter print projected in perfect focus" in your living room. Must get Blu-ray player. Amazon has the Blu-ray version for a whopping 50% off the retail price...it's almost the same price as the DVD version.
Update: The author of the Times piece has two before-and-after stills from the first film on his blog. Wow.