I still think some of it has to do with the red trays in the collector's case. I bought a collection once with red trays almost every figure in there had a pink glow to it. May not be the only reason but I think it definitely helped the process along.
There's a number of very detailed explanations for the degradation somewhere here in the forums but I don't have it bookmarked (I really should). In summary though, the chemical compounds in plastic breakdown over time and result in discolouration, brittleness, tackiness, splotching or any combination of these issues.
As blue_snag also highlighted, contact or proximity with different plastics can result in transference of colour.
Typically, the compound used for limbs is more susceptible to these issues due to the type of plastic used for flexibility and white plastic is notorious for degradation due to the specific compounds used for white plastic.
Causes for these issues can range from different degradation profiles as a result of different plastic compounds (remember, these things were produced in multiple different factories across many different years), through to environmental factors such as heat, humidity, exposure to UV, exposure to acidic cardboard or other plastics off-gassing.
Once the plastic has started degrading you really can't reverse the chemical reaction. Some will swear by peroxide for white items but this has been shown to cause other issues, particularly making hard plastics very brittle and usually the degradation will reappear over time. So all that has been accomplished is a visual whitewash for a few years and then actually added to the problems. So don't do it.