Gemara

(Rav Nachman bar Yitzchak): R. Meir fines one who damaged b'Shogeg due to one who was Mezid (lest he say that he was Shogeg). R. Yehudah does not fine.

Contradiction (Beraisa - R. Meir): If one cooked on Shabbos b'Shogeg, he may eat it. If he was Mezid, he may not eat it;

R. Yehudah says, if he was Shogeg, he may eat it after Shabbos. If he was Mezid, he may never eat it;

Answer: R. Meir fines Shogeg due to Mezid regarding mid'Rabanan Isurim, but not regarding Torah Isurim. R. Yehudah fines Shogeg due to Mezid regarding mid'Oraisa Isurim, but not regarding mid'Rabanan Isurim.

Question (Beraisa - R. Meir): If one planted on Shabbos b'Shogeg, he may let it grow. If he was Mezid, he must uproot it. If he planted in Shemitah, in either case he must uproot it;

R. Yehudah says, if he planted in Shemitah b'Shogeg, he may let it grow. If he was Mezid, he must uproot it. If he planted on Shabbos, in either case he must uproot it.

The Tana'im are inconsistent. Shabbos and Shemitah are both mid'Oraisa!

Answer (for R. Meir - Beraisa - R. Meir): Regarding Shemitah he must uproot it, because Yisraelim count the years of Shemitah (if they see him redeem Neta Revai four years from now, they will know that he planted in Shemitah and come to permit this). There is no such concern regarding Shabbos. Also, Yisraelim are suspected to transgress Shemitah, but not to transgress Shabbos.

Answer (for R. Yehudah): In R. Yehudah's area, people were very stringent about Shemitah (so we are not concerned lest they transgress it).

Question (Beraisa - R. Meir and R. Yehudah): (Parech nuts, an esteemed species, are never Batel in a mixture. If forbidden Parech nuts were mixed with permitted nuts,) if the nuts fell and broke, whether this was Shogeg or Mezid, the mixture is still forbidden.

Mid'Oraisa, any minority is Batel. Mid'Rabanan, important things are not Batel, yet R. Yehudah fines!

Answer: There, he fines lest one scheme to make them fall to Mevatel them.

Shabbos 38a (Rav): At first, the Halachah was that if one cooked on Shabbos b'Shogeg, he may eat it. If he was Mezid, he may not eat it. The same applied to one who was Meshaheh (left uncooked food on a fire at the start of Shabbos);

Many people did Shehiyah b'Mezid and said that they were Shogeg. Chachamim decreed to forbid even if one was Shogeg.

Chulin 15a (Rav Chanan bar Ami): Rav would rule to his Talmidim like R. Meir. In public he ruled like R. Yehudah, due to ignoramuses.

Beitzah 24b (Rav Papa): The Halachah is, if a Nochri brought a gift for a Yisrael on Yom Tov, if some of the species are attached (to the ground), they are forbidden until the time needed to do so (detach and bring them) after Yom Tov;

If none of the species are attached, they are permitted only if they were brought from inside the Techum.

Rishonim

Rif (Shabbos 17a, also brought in Rosh Chulin 1:18): The Halachah follows R. Yehudah, who says that if one cooked b'Shogeg, he or others may eat it after Shabbos. If he was Mezid, others may eat it after Shabbos, but he may not.

Rosh (ibid.): The Ri says that the Halachah follows R. Meir. The Ge'onim say that nowadays we expound in public to ignorant people, so we rule like R. Yehudah.

Rambam (Hilchos Shabbos 6:23): If a Yisrael did Melachah on Shabbos b'Mezid, he may never benefit from it. Other Yisraelim may benefit from it on Motza'ei Shabbos immediately. If a Yisrael cooked on Shabbos b'Mezid, others may eat it after Shabbos, but he may never eat it. If he was Shogeg, he or others may eat it immediately after Shabbos. The same applies to everything similar.

Rosh (19): In Beitzah (24b DH ul'Erev), Rashi says that one may never benefit from what was brought on Yom Tov lest he benefit from Meleches Yom Tov. This is unlike the Ri's Pesak like R. Meir.

Suggestion: Perhaps we are more lenient about cooking, for the food could have been eaten raw without Meleches Shabbos.

Rejection (Rosh): If one slaughtered on Shabbos b'Shogeg and there was a sick person in the house, R. Meir permits eating it. He does not forbid benefit from Meleches Shabbos. Even R. Yehudah forbids because he decrees Shogeg due to Mezid, but not due to benefit from Meleches Shabbos. All the more so we are not concerned for Meleches Yom Tov when a Nochri brings for a Yisrael. I say that the concern is lest a Yisrael ask the Nochri to do so for him on Yom Tov. Therefore, what a Nochri brought on Yom Tov Rishon is forbidden even on Yom Tov Sheni of Chutz la'Aretz. Rashi permitted, for one of the two days is Chol, so he does not benefit from Meleches Yom Tov.

Hagahos Ashri: If there are attached fruits of a species, and we are unsure if they were detached for a Yisrael or for Nochrim or if they fell by themselves, they are forbidden, lest a Yisrael detach them or tell a Nochri to do so. This refers to fruits that people covet and are easy to pick. It is an exertion to dig up turnips or trap fish, so we do not decree about them. Similarly, juice that exuded from fruits is forbidden lest one squeeze, even if the fruits were intended to be eaten. According to the Ri, if food was already k'Ma'achal Ben Drusai (a third or a half cooked) and a Nochri finished cooking it, it is not clear if we forbid. Perhaps we are not concerned lest a Yisrael would tell him to do so, since it could be eaten the way it was.

Poskim

Shulchan Aruch (OC 318:1): If one cooked on Shabbos (Rema - or did any other Melachah) b'Mezid, he may never eat it, but others may eat it immediately after Shabbos.

Gra (DH Oh): The Rambam and Shulchan Aruch forbid only Melachos, for even R. Yehudah forbids only regarding mid'Oraisa transgressions. We are stringent about one who transgressed Shehiyah because he will come to scheme (and say that he forgot). I proved above from the Yerushalmi that R. Meir does not fine regarding mid'Oraisa or mid'Rabanan.

Bi'ur Halachah (DH ha'Mevashel): We find that R. Yehudah does not fine Shogeg due to Mezid regarding mid'Rabanan transgressions. I do not know a source that he does not fine Mezid.

Kaf ha'Chayim (7): The Mishbetzos Zahav (1) forbids a Melachah mid'Rabanan even b'Shogeg the same day. The Gra and Chayei Adam permit. If it was Mitzvah, the Chayei Adam forbids even to others until Motza'ei Shabbos. However, if food was taken outside the Techum we do not forbid even to the one who took it, for the food did not change.

Mishnah Berurah (2): If there is any argument about whether or not something is considered cooking or any other Melachah, we do not forbid because the Isur of benefit from Meleches Shabbos is mid'Rabanan. We are lenient about a Safek mid'Rabanan.

Kaf ha'Chayim (8): The Levush says that if he was Mezid, the Isur to benefit from it is mid'Oraisa. This is difficult.

Kaf ha'Chayim (8): One may not benefit from the Melachah itself, but he may benefit from money paid for it. One may sell the item only for its value before the Melachah was done. If not, Chachamim's fine is pointless!

Shulchan Aruch (ibid.): If he was Shogeg, it is forbidden on Shabbos also to others. After Shabbos it is permitted also to him immediately.

Magen Avraham (3): One who followed a Hora'ah of a Chacham or forgot is called Shogeg.

Mishnah Berurah (7): When necessary one may rely on Tosfos and the Gra to permit on Shabbos when the Melachah was b'Shogeg.