The 35mm cinema frame is less than half the size of the 35mm photo frame.
The photo frame, as you know, is 36mm X 24 mm. The cinema frame is 20.96mm wide and can vary from 11.33mm (AR 1.85 "Widescreen") to 17.53mm tall. (AR 2.39 "Cinemascope")
The film runs through the camera or projector vertically instead of horizontally as it does in a camera. Those frames fly by at a rate of 24 per second. Other than that, the 35mm film used in the cinema is virtually identical, in physical dimensions, to 35mm photo film. There are some differences in the emulsions but it is possible to use 35mm cinema film in a still camera.
First, you have frame size and film speed to contend with. There is just that much less surface area to get dirty. Small bits of dirt are just that much harder to see. They are there but they are flying by at 24 fps. You CAN see them if you look hard enough but 90% of the people never even know it.
Then, just as David says, the resolution of a DVD is only 720 pixels wide by 486 lines tall. (Assuming non-anamorphic picture.) One frame of 35mm film has the equivalent of 4,000 lines, vertically. What dirt is on the film won't be registered if it is small enough.
After that, there is interlacing to deal with. One frame of a television picture is actually made up of two fields, each carrying half the picture. Theoretically, you never see more than half the picture at any one time. Persistence of vision creates the illusion that you see it all.
(The exception is if you are watching progressive content on a screen capable of displaying it.)
Hollywood studios also employ people to keep film processing laboratories and equipment scrupulously clean. A lot of times, they use "wet gate" techniques which clean the film with optically clear fluids and leave it wet while it is being projected.
The bottom line is that Hollywood movies really are that much cleaner and, because of the inadequacies in the resolution of television, what dirt does get through just isn't seen most of the time. It is there. You can see it but you really have to look for it.