I am a bit confused about the difference in Chapter 9 of Nedarim between a Petach found because of a neder based on mistaken facts and one based on changed circumstances (nolad). It is my understanding that the neder based on a mistaken fact is null and void, ab initio. Does this mean that we need to have the neder annulled or that since it was null and void as of the time being made, we do not need to have it annulled since it never took effect?
The Nedarim you are referring to fall into three categories.
(1) There are Nidrei Ta'us which are based on a total mistake, such as a Neder not to marry someone because she is short when she is actually tall. This does not need a Pesach at all.
(2) Nolad is when circumstances change in the future, in which case we are not Matir the Neder. Every Pesach must be based on the fact that the Noder would not have made the Neder had he been aware of the circumstances being used as grounds for the Pesach. However, Nolad could not have been known, and therefore the Noder definitely wanted the Neder at the time that he made it.
(3) The Mishnah states a case where the circumstances changed, and still it is not considered Nolad. Rav Huna says that since he expressed the circumstance in the Neder itself it is as if it was conditional and therefore when the circumstances change the Neder is void. Although the Neder took effect it does not need a Pesach for it was contingent on the circumstances remaining the same.
Rav Yochanan explains the Mishnah as referring to where the circumstances had already changed at the time of the Neder, and it is therefore a classic Ta'us and does not need a Pesach.