What are the implications of the word "Pis'om"?
Rashi and Ramban #1: It implies that the call came suddenly 1 and caught them by surprise.
Ramban #2 (citing Targum Onkelos): It implies 'immediately', 2 inasmuch as Hashem took them to task straightaway, without a moment's thought. 3
Rashbam: It implies that they were talking about Moshe, and it was not the time that Hashem would normally have appeared to them, and He only did so in honor of Moshe.
Why did Hashem call them suddenly?
Rashi: In answer to their criticism of Moshe - because they were Tamei after being with their spouses, and had to quickly find a Mikvah to Tovel - thereby driving home the difference between themselves and Moshe who had no fixed time to speak with Hashem, and never knew when Hashem would call him. 1
Ramban: Because they were not prepared for prophecy and Hashem appeared to all three of them simultaneously only in honor of Moshe ? and, whereas they were not prepared for prophecy, Moshe was.
Da'as Zekenim and Hadar Zekenim: So that they could not ask Moshe to Daven for them [to spare them from punishment].
Sifri: So that Miriam and Aharon should not think that Moshe had complained to Hashem about their conversation and Davened that He should take his part.
See answer #2.
What are the implications of the word "Shelosht'chem"?
Rashi: It implies that Hashem called Moshe, Aharon and Miriam in one Dibur, which was divided into three, so that they all heard it at the same moment. 1
Rashi: Something that no human-being can possibly emulate. Oznayim la'Torah: This was necessary because, Hashem was appearing to them by day, and, unless Aharon and Miriam would receive part of the Dibur that was said to Moshe, they would not be able to receive it at all, seeing as other than Moshe, all Nevi'im could only receive a Dibur at night-time. See Oznayim la'Torah.
Seeing as Hashem did not intend to speak to Moshe, why did He call him?
Rashi (K'sav Yad Teiman): He wanted him to be there in order to Daven for a Refu'ah Sheleimah for Miriam. 1
Ramban: He wanted Moshe to be there when he scolded Miriam and Aharon, to see how He (Hashem) was zealous on his behalf, and for him to be available to pardon them, since He would not do so without his consent, after they pleaded with Him and He was appeased. 2
Seforno: Because He wanted him to know about His goodness, how He cared about his Kavod.
Rashbam: To show Moshe Kavod, because He was scolding Miriam and Aharon on his account. 3
Why does the Torah add the (otherwise superfluous) word "Vayeitz'u Sheloshtam"?