What are the implications of the word "Pis'om"?
Rashi: It implies the call came suddenly 1 and caught them by surprise.
Ramban: Because the root of "Pis'om" is 'Pesi', with reference to something that did not enter one's mind. Refer also to 12:4:2:2. The Torah uses the word in connection with Aharon and Miriam, because Moshe was prepared for Nevu'ah at all times.
Why did Hashem call them suddenly?
Rashi: He did it in answer to their criticism of Moshe - because they were Tamei after being with their spouses, and had to quickly find a Mikvah to immerse - 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.
Ramban: Because they were not prepared for prophecy and Hashem appeared to them only in honor of Moshe.
Da'as Zekenim, Hadar Zekenim: This is so they could not ask Moshe to pray for them [to spare them from punishment].
What are the implications of the word "Sheloshtechem"?
Rashi: It implies that Hashem called Moshe, Aharon and Miriam independently all at the same moment. 1
Rashi: Something that no human-being can possibly emulate.
Why did Hashem call Moshe?
Rashi (K'sav Yad Teiman): Although Hashem did not speak with Moshe, He wanted him to be there in order to pray for a Refu'ah Sheleimah for Miriam.
Ramban: He wanted Moshe to be there when he scolded Aharon and Miriam, 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, when they would plead with Him and He would be appeased.
Seforno: Because He wanted him to know about His goodness, how He cared about his Kavod.
Rashbam: Because He was scolding Aharon and Miriam on account of Moshe, and to give Moshe Kavod.