Research for photographing projections:
"Okie dokie, so the answer may have been too simple. It actually depends on the projector and the screen. Typically projectors that do digital images display at a rate of 60hz on refresh. This means the optimal shutter speed should be about 1/15. Why? I actually have no idea. Something to do with fighting the refresh on the LCD that is responsible for showing the image. Light can "bend" due to the screen used and due to how the image is projected. The problem with projected images is that the light is dispersed to the screen at wider angles in order to get the image blown up on the screen or wall. The refracted/reflected light will undoubtedly change the color and frequency of the light going into your camera. For this reason, I suggested that you pretty much be "on top" of the projector to reduce the amount of light bouncing around. So other than that, I would adjust your white balance to match the screen. Oh, and for practice, you can turn on live view on whatever you're using to get onto FM and adjust the shutter speed until you don't see the issues you mentioned."
"60hz would be 60 updates per second. so I would think that any shutter speed below 1/60 should be fine. This is the same thing for shooting under florescent lights as they are also around 60hz."
"If it's 60hz, you want to make sure to capture a whole number of cycles, i.e. 1/60, 1/30, 1/20, 1/15, 1/10.... I'm guessing that 1/15 is cited as the best time because of minor discrepancies between the projector and camera in terms of exact fractions of seconds."
"DLP projectors have a spinning color wheel in front of the micromirror device. Basically it can only display one color at a time so it cycles through all of the colors it needs in fast succession so that it all looks like a single full-color image to the human eye. If your shutter speed is too fast it'll only catch a portion of the projected image. Keep your shutter speeds low (~1/10-1/20th) to avoid the issue.
LCD projectors don't have the same problem."