Gemara

(Mishnah): We are Pose'ach with Shabbos and Yom Tov (he overlooked that his vow will include these days).

At first, Chachamim permitted those days and forbade other days. Later, R. Akiva taught that a vow that was partially permitted is totally permitted.

Rishonim

The Rif and Rosh (8:5) bring the Mishnah.

Ritva (DH Poschin): He forbade a food for many days. He thought that Shabbos and Yom Tov are not included in his vow. He said 'had I known, I would have specified only weekdays.'

Rambam (Hilchos Nedarim 4:11): If one swore or vowed 'I will not give benefit to all of you', and permitted his vow or oath regarding one of them, all of them are permitted, because a vow that was partially permitted is totally permitted.

Perush ha'Rosh (66a DH sheha'Neder): Even if he did not find a Pesach for the entire vow, he vowed only with intent for the entire vow. Therefore, permitting part is a Pesach for the entire vow.

Ran (DH she'Kol): The Yerushalmi learns from "k'Chol ha'Yotzei mi'Piv Ya'aseh" that it is (a binding vow) only if the entire vow is in force.

Poskim

Shulchan Aruch (YD 229:1): If a Neder was partially permitted, it is totally permitted.

Rivash (291, brought in Beis Yosef DH Kosav): If one swore not to eat figs or grapes (or drink two drinks), and permitted one food (or drink), both are permitted. If one forbade two activities, e.g. eating and wearing drinking, and permitted one of them, the other is forbidden (for this is like two vows). It seems that the same applies to eating and drinking.

Shulchan Aruch (ibid.): If one vowed to fast or to eat meat for a certain time, and Shabbos or Yom Tov occurred, we ask if he would have vowed had he considered this. This permits everything.

Beis Yosef (DH uv'Ha): The Rosh (DH Masnisin) says that Shabbos and Yom Tov are Pesachim for vows to fast or not to eat meat. The Tur mentioned only fasting. He holds that they are not Pesachim for meat, for one can fulfill Oneg Shabbos with a fish dish (without meat). The Rambam holds like the Rosh.

Rebuttal (Taz 2 and Bach DH Aval): Surely, not eating meat reduces Oneg Shabbos, and one may Pose'ach with this! The Tur merely cited one case.

Shulchan Aruch (ibid.): Some say that a vow is totally permitted if he permitted part through a Pesach, but not if he permitted part through regret. Some say that in either case it is totally permitted.

Beis Yosef (u'Mah she'Chosav v'Afilu): The Rosh and Ramban say that even when he was Kolel (forbade all together), the rest are permitted only if he permitted part through a Pesach. This makes the Neder like a mistake from the beginning. If he permitted part through regret, the rest are forbidden. The Ran(27a DH v'Chosav) says that Tosfos totally permits in either case, since a Chacham permits retroactively. Perush ha'Rosh (66a DH Konam) is like Tosfos. The Tur adopts the Rosh's opinion in his Pesakim, like the Ramban.

Ran (27a DH v'Chosav and Rivash 453, cited in Beis Yosef DH veha'Rivash): Even Tosfos permits the entire vow only because a Chacham permits retroactively. Therefore, if a husband annulled part of a vow, the rest stands.

Shulchan Aruch (ibid.): This is only regarding one who vowed by himself. If he vowed or swore to Ploni to pay him or do a job for him and Ploni permitted part, the rest is not permitted. The same applies if there were two and one of them was permitted.

Beis Yosef (ibid.): R. Yerucham (14:7:113b) says that if one vowed to Levi and cannot permit his vow without him, e.g. to do a certain task or pay a debt, if Levi permitted part, the rest is forbidden. The same applies if he vowed to Levi and David, and Levi permitted his part. Many err and say that the entire vow is permitted.

Taz (5): Ploni permits by saying 'it is as if I received.' Since the Noder was obligated to pay the full amount, Ploni does not lose the rest if he pardons part.

Bach (DH v'Im): In Siman 232, the Tur permits the entire vow only if he would have been Meshaneh (vowed differently) had he known. The Tur did not require this here. The Ran and Rosh (25b DH Tanan) say that when the entire vow was a mistake, e.g. he forbade people eating his fruits and never intended for his father, the vow is Batel automatically. One who vowed for a year knew that Shabbos and Yom Tov will occur, just he did not know that one may not fast then. The vow takes effect; a Chacham can permit it. In this case, we do not require Shinuy. I cannot explain why the Rosh (25b DH Omar) requires Shinuy also regarding fasts. However, the Ramban requires Shinuy even regarding fasts. The Beis Yosef (232 DH v'Chosav ha'Ran) cites the Ran (Reish 27a), who concludes like the Ramban. However, in Shulchan Aruch here he did not specify, implying that no Shinuy is needed. The other Poskim agree.

Shach (4): Also Darchei Moshe (232:5) says that when one must ask a Chacham, the Tur does not require that he would have vowed differently.

Rebuttal #1 (Birkei Yosef 232:2 DH v'Ashkotah): The Ran and Rosh only said that regarding fasts, the vow took effect. They did not discuss Shinuy. The Beis Yosef holds that the Tur here relied on what he wrote in Siman 232. The Shulchan Aruch did similarly!

Rebuttal #2 (Taz 5): The Beis Yosef (232 DH v'Chosav ha'Ran) cited the Ramban and Ran to say that the entire vow is permitted only if he would have vowed differently had he known. One must be stringent like this, for no one explicitly disagrees. Also Darchei Moshe rules like this.

Note: The Darchei Moshe (229:2) says 'see Siman 232, that it is totally permitted only when he would have vowed differently.' This connotes that the same applies here. However, there (232:5) he said that the Tur distinguishes.