Rashi: The current Pasuk is referring, not to the time-period of eating Shelamim, ¹ but to the issue of Pigul - if, when slaughtering it, one has in mind to eat it after the specified time-period, it becomes Pigul and may not be eaten. ²

Rashi #1: It means that the Shochet should not render the Korban Pasul by having a wrong intention whilst Shechting it. ¹

Rashi #2 (citing Chulin, 13a): It means that if one Shechts a Korban unintentionally, the Korban is Pasul. ²

Rashi #3 (K'sav Yad Teman) and Ramban: It means that when Shechting a Korban, one should Shecht it in a way that one gains a Kaparah through it ³ ('for your goodwill', ⁴ by bringing it with the intention of eating it on the day it is brought and on the following day and the night in between - Rashi in K'sav Yad Teiman).

Rashbam: It means that the Korban should be without blemish and that one should bring it to the entrance of the Ohel Mo'ed, and that the owner should lean his hands on it and comply with all the other required specifications that the Pasuk goes on to list.

Menachos, 110a: 'Hakadosh-Baruch-Hu said to Yisrael; "It is not for My sake that you bring Korbanos, but for yours - so that you should have a Kaparah!'

Seforno: Refer to 19:2:2:3***. The Torah is teaching us here, that, in keeping with "Anochi Hashem Elokecha", it is not sufficient to keep His Mitzvos and to exalt Him as they undertook to do, ¹ and to pray to Him in times of trouble, but that one also takes care to honor Him in thought, by not desecrating His Holy objects with wrong thoughts.

Chulin, 29a: To prohibit Shechting two Kodshim animals simultaneously. ¹

Ramban #1 and Moshav Zekenim #1: Because we learn other Korbanos from the Shelamim with a Kal va'Chomer - If these Dinim apply to a Shelamim, which is Kodshim Kalim that are eaten by the owner, how much more so will they apply to Kodshei Kodshim, which are eaten by the Kohanim.

Ramban #2 and Moshav Zekenim #2: Because esoterically, 'Shelamim symbolize the Midah of Yisrael'. ¹

Oznayim la'Torah #1: It is necessary to write this Din with regard to both Shelamim and Olah, ² since initially, Beis-Din may take a security, if necessary, against the wishes of the owner. Therefore the Torah needs to teach us that when doing so, they must make sure that the owner gives his consent. Chayvei Chata'os and Ashamos on the other hand, where the owner brings his Korban on his own initiative, it is obvious that he agrees, and it is therefore unnecessary to mention the Din of Ratzon.

Oznayim la'Torah #2: The Torah mentions the Din of Ratzon specifically by Shelamim, from which the owner derives personal benefit - and which he therefore needs to be reminded to bring it for the sake of Hashem, as opposed to an Olah, Chatas and Asham, from which he does not benefit, and for which a reminder is therefore not necessary. ³

Oznayim la'Torah #3 (according to the Rambam - who gives the reason of Korbanos as - to counter the Nochrim who bring sacrifices to their deities): After writing "Al Tifnu el ha'Elilim", the Torah adds that, if and when we bring Korbanos, we should bring them in the Name of Hashem, and it mentions Shelamim which Nochrim are not eligible to bring.

Oznayim la'Torah #4 (according to the Ramban, who disagrees with the reason of the Rambam) ⁴ : After stating the Mitzvah of Kedoshim Tih'yu, ⁵ we find that Yisrael attained it by the Mitzvah of eating the Korban Shelamim which they brought in the Name of Hashem, and which Hashem then invited them to eat at His Table.