No, you shouldn't. That is, unless you don't want to see the film released in HD for the next few years, or maybe not released at all!
White specks generally come from dust on a negative or internegative film element, created during the film's original production. Likewise scratches can be introduced in any of the myriad steps of creating the film element used for the transfer to video.
The studio has two alternatives, release the title as it was shown in it's original presentation in the theater including the white specks with maybe a few scratches here and there, or put it through expensive and time consuming "dust busting" and scratch removal processes.
On a marginally performing title, which includes almost all the catalog titles, the extra cost and effort of these processes could very well cause the studios to either delay or never relase the BD at all.
I'll take some white specks and a few scratches on a BD any day over never having a BD release at all.
Dirt and Dust removal and DNR for grain reduction are generally not the same thing.
D&D removal is an algorithm that searches for specks above a particular size limit that exist on only one frame. The software then removes that particular spot using information from either the frame before or the frame after. It does not soften the images and should have no effect on the grain of the film when set up correctly.
Sometimes this is the case, but I have seen wonderful examples of D&D remove where this was not the case. Of course Casablanca is one example as is Forbidden Planet. Warner in particular seems to be very careful in this regard. The Sting is another film where clean up has been done but the grain hasn't been touched at all.
Suddenly it's become a vogue to bitch about DNR--but I remember no one complaining when Con Air came out, which was virtually grain-less. In many scenes during that movie Nic Cage's face looked waxy, plastic. But no one complained because a 'pro' came and made a thread about it. If a print is three generations old, some DNR is necessary--not all grain is sacred. I remember James Cameron saying after watching his film Aliens years later he was surprised by how grainy it was--so no, most of the grain in the picture is not the director's intent.
I’ve never seen Con Air so I can’t comment one way or the other—but if the movie were released with little or no grain, then there would be no reason to complain, as that would have been the filmmakers’ intent. OTOH, if you are referring to a DVD release where the grain had been removed, again I suspect that many would have complained just as they did about such DVD releases as Citizen Kane that had been cleaned up way too much. Con or Kane it makes no difference—both films deserve to be presented as the makers intended.
While I don’t recall exactly how much grain was in Aliens, I first watched in during its initial run and it had quite a bit of grain. There is a difference between restoring as closely as possible to what was shown originally and removing that which was present the first time around.
As a further comment, it has not suddenly become in vogue to complain about DNR. Many members on this forum (as well ones like the Digital Bits) have raised issues such as grain removal, edge enhancement and other electronic tricks that detract, rather than enhance the transfer.
Sure, you´re not all wrong here. I believe the point is too keep everything (also grain) in balance and as "natural" as they can (for each film - the styles differ greatly). Still, in Blu-ray transfers like "Patton", removing ALL the grain is probably not the way to approach these type of issues..
My personal opinion is that speckles and especially scratches should be removed transparently (e.g. not touching actual image content and grain) for an optimally restored picture, but if some stay in it's ok as it is very common and perfectly compatible with the film look. Distracting scratches (colored ones, big ones, standing ones, affecting the focus of attention) should be removed as they affect the esthetic impact of the picture and can severly disrupt the viewing pleasure. If speckles and dust can't be removed without touching actual image content (for budget reasons or whatever) they should stay till they can be properly fixed.