Inspired by the comments, I have a possible answer for the confusion between didn't used to and didn't use to. In general American, I used to is pronounced with an /s/, while I use or I used in other constructions is pronounced with a /z/. I didn't use to is also pronounced with an /s/, but I believe this may be the only time that /use/ is pronounced with an /s/ and not a /z/, so it is a very understandable mistake to transcribe I didn't use to as I didn't used to. As far as I can tell, the /justə/ (or /justu/) part of I didn't use to and I used to are pronounced exactly alike. Except for not giving the pronunciations, this is pretty much what NOAD says, as quoted in Jimi Oke's answer.
A Google Ngram for American English is very enlightening:
People are now usually spelling didn't use to as didn't used to, and this construction is replacing used not to. For British English, you can do the same thing, and you find that while the construction in the UK is still generally used not to, the ungrammatical spelling didn't used to is replacing the grammatical spelling didn't use to.