But to bring the discussion back to the OP's question, some of my bars develop individual spots of orange color, but other bars don't -- even in the same batches. Individual spots can come from so many random sources -- oxidized bits of FOs, EOs or other additives as others have pointed out. They can also come from particles of metals, dust contamination, or tiny bits of whatever. I can't blame myself too much for this type of DOS, although I keep working on ways to minimize the appearance of these spots.
Vitamin E has been shown by Kevin Dunn to
not be very effective in preventing oxidation (rancidity) of oils. Better options are ROE (rosemary oleoresin), sodium citrate, tetrasodium EDTA, and BHT. These anti-oxidants and chelators are effective protection. According to Dunn, adding 1 gram of ROE to every 1000 g of oils right after you buy the oils is a pretty effective way to minimize DOS. And it's a good option for those looking for a "natural" solution to this problem.
If the color change and rancid odor covers pretty much the entire bar, inside and out -- that's pretty clearly rancid oils or some another ingredient that is going bad, IMO. I traced a case of overall rancidity for one whole batch of CO-lard soap to my use of lavender EO that I didn't realize was oxidized.
I also found in a very personal way recently that overall rancidity and color change can be related to how soaps are stored. A few months ago, my girlfriend showed me some of the soaps I'd given her over the years. They were all from different batches and different ages and different packaging (or no packaging). All of the "naked" bars I'd given her were horrifyingly orange-yellow and smelled funky, but the bars I'd packaged in shrink wrap were fine. I gently but firmly swallowed my embarrassed reaction and gathered up all the bad bars. When I got back home, I frantically looked at the samples I'd kept in my "bone pile stash" from these same batches. The sample bars in my bone pile were all fine! She was storing her soaps in an old cardboard box, so I figured it might have been acids or something from the cardboard that was creating the problems. I now shrink wrap all of my soaps and will keep a careful eye on them as time goes on.
SoapSmith did a test of storing soap in various ways that showed similar results:
http://www.artfire.com/ext/shop/blog_post/Soapsmith/136/soapsmith_s_dos_experiment