The Rainbow Effect often referred to as RBE, is a "stroboscopic" affect that has some people seeing flashes of red green and blue. This is caused by the eye/brain dealing with the effects of projectors using high speed, spinning, color filter wheels. Most color wheels have Red, Green, Blue, and sometimes a clear area, some others add yellow, and others due all six primary and secondary colors (red, green, blue, cyan, yellow, and magenta).
Since a color wheel is needed for this to occur, the only types of projectors affected are DLP projectors, since they are single chip devices, and require a color wheel to add color. The other two major projector technologies are LCD and LCoS, both of which use three chips (or more technically correct - three panels). There are 3 chip DLP projectors, which have no color wheels, but they start around $10,000 US.
Rainbow effect is most visible when bright white areas move quickly across a very dark background, or the other way around. The presence of white or near white is necessary to get the full effect. If for example the lighter color was green, there would be no red or blue component, to become visible.
Rainbow effect, first of all seems to affect only a small percentage of the population, and is mostly an issue with video, rather than static images such as a spreadsheet. Some people are very sensitive to RBE, while others only occasionally. Although there don't seem to be any good numbers on how many people are affected by RBE, that number is probably below 5%. I am somewhat susceptable. I find that on a typical DLP business projector (most have 2X speed wheels), RBE is very evident.
The traditional home theater projector, however uses color wheels of 4X (mostly some entry level home theater models, 5X - the vast majority of DLP home theater projectors, and 6X (only found on a few projectors - notably some Opotma projectors. I can state that RBE is more apparent to me (and therefore others) with a 4X color wheel, than a 5X, and even less visible with a 6X wheel.
With 6X wheels I may often only spot RBE several times during a full length movie, while 4X becomes visible frequently.
Some folks susceptable to the rainbow effect, don't mind it enough for it to affect their purchase decision. I for one, owned three single chip DLP home theater projectors in a row, covering four years. I learned to live with it as a minor annoyance, but felt that the occasional flash, was less of an issue, at the time, than say the drastically inferior black level performance of 3LCD projectors back 3-4 years ago.
One thing to consider, that many forget. Even if you are not at all susceptable, other members of your family, or circle of friends will be. Not a lot, but maybe one, or two.
In some ways yes. Some report that when they got their first projector it was very noticeable, but after a while, less so. I've read about a couple of people (who I will assume were just barely susceptable), who over time, stopped seeing RBE.
Most importantly, however, your own movement seems to trigger seeing RBE. For example, someone reported that they only saw it when munching on popcorn or other snacks. Basically head and eye movement can make it more visible to you. I can confirm that chewing increases my ability to see it, as does shaking my head, or even moving my eyes quickly from one side of the screen to the other. Remember though, you also need the right conditions - white across dark, or the other way around. You aren't going to see it on a bright scene of sunny fields, but watching a car chase on a wet night is going to have a very high probability.
One last thing - I notice that I am more susceptable when very tired.
OK, that pretty much covers the Rainbow Effect. You will have to determine, first of all if you or your immediate family is susceptable, and if any are, you weigh the trade-offs against non-DLP projectors.
Remember, it takes certain types of scenes for most who can, to actually see RBE. So, it's not like it is ever present, even with those most effected.