The point of using a multiple of 24 is based on a few assumptions. Many have pointed out that 120Hz is the best choice of refresh if the projector supports it. This is because 120 is a multiple of 60 and 24...
OK, so why 72 or 120 or any multiple or 24? The assumption is that the software is doing a pulldown to produce a real 24p image. How the video card in the computer manipulates the overlay buffer (video buffer being refreshed by the DVD software) comes into play here. If the overlay buffer is being redrawn when the video card is updating the screen then overlay buffer tearing can occur. This is not such a huge problem anymore since there are methods of synching the video overlay updates with the screen refreshes, but with older cards and older drivers it is still known to happen.
The second issue with using a refresh rate that is not a multiple of 24 is the judder introduced by the video overlay update delay while waiting for refresh. The overlay buffer is locked during a screen refresh to prevent tearing, and the overlay update must wait for the next refresh to be displayed. Worse case is that a frame of the movie will be almost 2 screen refresh periods late if the timing is just right. At 60 Hz that's 1/30th of second which is noticeable. So, it's better to have a multiple of 24 if you want the minimum judder from overlay updates. Unfortunately, there are other sources of judder that come from the DVD decoding software, system drivers, AGP bus issues, etc... It's a tricky thing to get right.
So given the case that the video card is correctly displaying a video overlay with minimal judder introduced by other sources it up to the projector to correctly display the image. At this point things get complicated since there is no set technique that all manufactures seem to use. Early projectors only would sync a fixed set of refresh rates. This approach kept things simple, but it made setting up the projector a little more challenging.
Modern projectors will sync a wide variety of refresh rates and resolutions. In order to achieve this two things need to occur. 1) Video scaling 2) Frame rate conversion.
Now, different projectors do better or worse in either category. There doesn't seem to be much in the way of consistency between manufactures or even with a product line of a given manufacture. Knowing where the sweet spot is for a given projector can be difficult. But, as a rule of thumb the resolution of the computer should match the native panel resolution of the projector. This is simply due to the poor scalers built into most projectors.
With few exceptions, almost any modern graphics card will scale an image much better than a projector. In some cases, a modern graphics card can scale a DVD image better than professional equipment costing several thousand dollars. This is a case of the video card industry spending millions of $$$ on R&D for 3D graphics, building very complex and impressive graphics processing chips, and oh BTW this fancy hardware for games that just happens to be pretty good for displaying movies.
OK, so the frame rate conversion is where the video card / projector issue really gets interesting. The frame rate conversion is necessary because almost all projectors (LCD, DLP, LCOS, but not CRT) want to operate at a set internal frame rate. Many DLP have color wheels which spin at a set rate. This sets the fundamental refresh rate of the such a projector. Other DLP projectors had variable spin color wheels and could match the rotation of the color wheel to the video refresh rate. In some ways the electronics of the projector is made a little simpler but the mechanics of the projector are more complex. At any rate, it's not as common today and most DLP seem to be using a fixed spin rate color wheel and triple buffering to solve this problem. Some older projectors used fixed spin rate color wheels and double buffering. These projectors exhibited lots of tearing if the refresh rate of the computer was not matched to the native refresh rate of the projector. Even if they were matched there is nothing to keep them synchronized and tearing can still occur.
LCD and LCOS projectors don't use color wheels but still generally operate at some fixed internal frequency. The reason in this case is that the switching speed of the LCD and LCOS material is fairly slow and trying to force the material to switch too quickly produces bad results. I have no idea what frequency a given projector may be working at, but it would be a safe idea to assume something like 60 Hz for most application and MAYBE 72 Hz if it detects film based video. That's not to say that some manufactures don't adjust the internal refresh rate to match the source, but at a certain point the actual display panels will not be able to keep up if the output of the video card refreshes faster than the physical pixels on the LCD/LCOS panel can switch.
In the common case where the projector does some sort of frame rate conversion, the result can be tearing and judder if the projector does a bad job. Some projectors do a pretty good job (triple buffering again) and don't produce too many problems. It can take some experimentation to find the best refresh rate which minimizes the overall tearing and judder problem for a projector not that adept at dealing with video.
In the case where the projector is bad a frame rate conversion it is probably better to set the video card refresh to the setting which makes the projector happy. The overlay should maintain sync with the video card refresh if that part of the system is working right and this will prevent tearing (hopefully). Judder may or may not be better or worse with such a setup. My personal experience is that the judder from the computer is greater than any judder introduced by the projector. More particularly, judder from the video drivers and DVD decoder software can make horizontal pans less than smooth, but I've found judder much less of an overall issue now that I have the Cinemaster software DVD player with DXVA (Direct X Video Acceleration) and a Radeon based graphics card. So any frame rate conversion my particular projector is doing introduces very little judder.
