To what extent does film condition influence projected image stability? I've been projecting a number of trailers on my old (but cleaned and shined up - if anyone is interested in seeing a picture of this contraption, I'd be happy to provide the http…) Brenkert BX-40 and notice some of the films have virtually no observable "weave" or sideways wiggle on stationary credits. On other films this condition is more noticeable. I realize that some of this is related to the accuracy of the pulldown, and to test this I projected a pre-cropped (1.85+) flat film using an aperture (1.75) that was taller than the cropped image on the film. The projected top and bottom of the cropped image on the film on screen is absolutely rock stable. So that indicates to me the intermittent and intermittent sprocket are doing their thing properly.

Getting back to weave or apparent side motion, it appears to me the horizontal positioning of the film as it passes through the gate is REFERENCED to the outside edge of the film. (edge closest to the projectionist - sound track edge) That is: the film is held tight against the outside guide rail and this fixes the horizontal positioning of each frame as it is projected. Thus if the film width varies due to wear or other factors (maybe even unevenness of the original stock from Kodak or wherever) then there will be more observed weave. By the way, my guide rails appear to be in reasonably good shape and are not grooved or undercut.

Trailers often go though more stages of duplication than feature films. For example, a master positive is printed from the original negative, then a duplicate negative. This duplicate negative may be the film conformed (edited) to produce the trailer, perhaps along with material that has been digitally generated. A master positive is printed from the conformed duplicate negative, and another duplicate negative from this. Finally, the final prints are made, often using a high speed printer with the picture and sound negatives in a loop.

Many are quick to blame "high speed printing" as the source of any unsteadiness. But any stage of the duplicating process, if done improperly, can introduce unsteadiness. Time pressures often force film laboratories to use continuous contact printers for the making the duplicate negatives, where a much slower pin-registered step printer would give better steadiness.

A very good discussion of film laboratory procedures is in the "Dealing With A Laboratory" section of the Kodak publication "Eastman Professional Motion Picture Films: H-1", which is available for free download on the Kodak web site:
http://www.kodak.com/US/en/motion/support/h1/index.shtml