What do the inverted words "Vayachalmu Chalom Sheneihem" teach us?
Rashi #1: It means simply that they both had a dream. 1
Rashi #2: It teaches us that each one dreamt his own dream and the interpretation of that of his friend.
Ha'Emek Davar: In Chulin 92a, many interpret the dreams regarding Yisrael. They explain Sheneihem to be the Sar and his companion, i.e. Yosef.
As if the Torah had written 'Vayachalmu Sheneihem Chalom'.
What is the significance of the fact that the butler and the baker dreamt on the same night?
Oznayim la'Torah: It was the night of Rosh Hashanah, when most dreams come via an angel and are therefore significant. 1
See Oznayim la'Torah on 41:1.
Why does the Torah add "Ish k'Fisron Chalomo"?
Rashi: Each dream resembled the interpretation that would be given for it. 1
Ramban (citing the Ibn Ezra): Each one dreamt his dream and the events that Yosef ultimately interpreted, down to the last letter.
Rashbam: They were dreams that were worthy of interpretation, and not just meaningless ones.
Targum Yonasan and Berachos, 55b: Each one dreamt his own dream and the other one's interpretation.
Malbim: Each dreamed what was appropriate for him (about wine or bread). Further, it was appropriate for the Sar himself, and not for the worker under him. The Sar would put the cup in Pharaoh's hand or carry the baskets of baked goods.
Just like Pharaoh's dream resembled the interpretation given for it (as the Ramban explains below, 41:12). However see Ramban's objection to this explanation.
Why does the Pasuk repeat the fact that they were the Mashke and the Ofeh of Melech Mitzrayim, and that they were incarcerated?
Seforno: Even though they were important officers, the fact that they were in jail affected them negatively, and they dreamt like plain butlers and bakers.
Oznayim la'Torah: Because they were therefore unlikely to have thought about serving the king - a further sign that their dreams were (not merely what they thought during the day, but) dictated by an angel. 1
Malbim: The Sarim had the dreams, but they were proper for the Mashke and the Ofeh (the workers), who were in the same prison. I.e. the baker should have been killed for his great negligence, but the wine-maker deserved to live, for the fly was Ones. The dreams were not proper for the Sarim; Sar ha'Mashkim was more negligent than Sar ha'Ofim! (Refer to 40:2:151:1.)
Ha'Emek Davar: This is why Yosef interpreted according to the interpretation. If any of these were missing, he would not interpret so. 2 It did not depend on being Sarim, so they are not called Sarim.