Firstly, I only saw the movie, the score in the film didn't convince me so I'm not going to buy it in the close future (my principle is: "if I didn't enjoy the score as heard in the film don't hurry up with buying it" ), considering that Williams is my favorite and beloved number 1 composer for years I was simply dissapointed by the score and less by the film.But You talking here about "Blade Runner", one of my very best movies so...

> The opening part of the sound track by John Williams echoes that of
> Vangelis' score in Blade Runner (1982), with the booming noises and a
> black screen, before the opening scene fades in.

That's truth. Vangelis' opening title music sounded not from this world. Just simply synths, but has some power...

If Williams uses the
> same motif from Blade Runner, than so does the screnwriter:
References
> to Blade Runner (1982), also based on a written work by author Philip K.
> Dick.
Both films begin with an extreme close-up shot of an open eye,
> and repeat the eye motif throughout.

Yes, and the close-up shot in BR came trough the history of cinema already

Rutger Hauer's character (in
> Blade Runner) visits the genetic engineer who created his artificial eyes,> Tom Cruise's character visits the surgeon who replaces his eyes.

The diffrence is that in BR it was a Japanese, in MR it is Swedish (Peter Stormare, who originaly is Swedish)

Both
> films feature detectives making a key discovery by spotting a woman
> reflected in the mirror in the background of a crime-scene image that they
> are looking at.

Yes!Good observation! But the techniques are quite different. Cruise uses a 3-D some kind of a virtual screen ( I was rather overhelmed by all those virtual advertisements and other stuff in the film) and in Blade Runner Ford uses some fantastic photo-device, which stimulated our imagination lot better.

Several times, bright shafts of light pour in through
> the windows behind the characters as they talk; this effect was used
> extensively in the earlier film.

This was one of the things that made Blade Runner so unique and "atmospheric", but I must admit that Janusz Kamiñski's cinematography in MR is also brilliant (as always)

After Cruise's encounter with Crowe,
> he drives with Agatha through a gorgeous green scenery, and tells her
> they're going "Someplace safe", a scene which parallels the
> ending scene of Blade Runner (the original, not the Director's Cut
> version.

The difference is that they went by car and in BR they went by train

Finally my short conclusion is that with even all those similarities MR is a solid s-f extravaganza but IMHO will never reach the level of masterpiece which BR is (and yes,the Director's Cut is even better!) . Interesingly the A.I. which was a project of a late Kubrick made by Spielberg to almost masterpiece of s-f IMHO, I (and not only me I suppose) find there also couple references to Kubrick's old films. Additionaly Williams' score in A.I. was heart-breaking and simply awesome in compare to what he did in MR

Regards

Tomek