What was the gist of her complaint against her husband (See also 39:17)?
Ramban: The Egyptians hated the Ivrim, to the point that eating at the same table was considered an abomination. They would acquire them to work in the vineyards and as gardeners, but not to work in the house. Consequently, her husband 1 had wronged them all by bringing Yosef into the house and appointing him as manager, for him to jest with them. 2
Ramban: Whom she did not mention by name, either out of respect, or because it was obvious that that was whom she was referring to, as is common in Tanach (particularly in Sefer Iyov, it is often understood that when speaking in third person it discusses Hashem).
See Mishlei 29:21.
What did Potifar's wife ask the members of her household to 'see'?
Targum Yonasan: She placed the white of an egg of her bed and pointed to it, making out as if it was semen. 1
Ohr ha'Chayim #1: Here she was trying to incite her household against him, through envy - see, [my husband] raised a stranger over us!
Ohr ha'Chayim #2: See, so you can testify about this.
What does "L'Tzachek Banu" mean?
Rashi (to 21:9): 'Metzachek' is an expression of sexual immorality.
Ramban, Targum Onkelos and Targum Yonasan: It means literally 'to laugh at (to make fun of) us.'
Seforno: Potifar's wife was accusing Yosef of acting in a lewd fashion, which clearly indicated his intention of being intimate with her.
Why here, did Eishes Potifar say "l'Tzachek Banu," whereas below, when relating the incident to her husband (39:17), she said "l'Tzachek Bi"?
Oznayim la'Torah: Because here she was trying to incite all the people against him, 1 whereas when speaking to her husband she was stressing that Yosef accosted her - the most beautiful of women, in order to arouse his ire against him.
Malbim: She aroused them by saying - If he did so to me, all the more so he will do so to you!
Ha'amek Davar: She understood from Yosef's claims that he could not fulfill his desire with his master's wife for reasons (Hakaras ha'Tov, fear of demotion) that did not apply to the others; and that he truly enticed them to Zenus. 2
See Oznayim la'Torah.
I do not understand this. Yosef concluded "v'Chatasi lE'lokim" - this applies to Zenus with anyone! (PF) Ha'amek Davar (to 39:18) writes below, that Yosef in fact did himself a disservice by adding other reasons on to "v'Chatasi lE'lokim;" indeed it seems that she missed Yosef's point. Refer to 39:18:152:1*.
What is the significance of the loud voice? Why did she need to mention it?
Rashbam: As mentioned earlier, there was nobody in the house, since they were all celebrating. Consequently, had she not cried out loud (according to her version of the story), Yosef would have raped her.
Ha'amek Davar: It would be expected that one who is shocked at such enticement would scream in a loud voice.
QUESTIONS ON RASHI
Rashi writes: "Ivri - From the other side of the [Euphrates] River (Ever ha'Nahar); and from the descendants of Ever." Why does Rashi need to give both reasons? (On the verse "Avraham ha'Ivri" (14:13), on the other hand, Rashi writes only the first reason - that Avraham had come from across the river.)
Gur Aryeh: a) It had been almost 200 years since Lech Lecha, when Avraham crossed the river and settled in Eretz Kena'an. b) Why specify Ever as the ancestor of Avraham's family, rather than going back to Shem? 1 Thus, neither of the two reasons is sufficient on its own to explain why Yosef would be referred to as an Ivri; only the combination of the two reasons explains it. Once Avraham became known as "Ivri" for his journey from Charan, as well as being descended from Ever, 2 the name stuck on his descendants as well.