Why does the Torah omit linen from the list?
Rashi: This proves that "Bigdei S'rad" are not the Bigdei Kehunah - which contained linen, but the cloths with which they covered the Holy Keilim (at the end of Bamidbar). 1
Why does the Torah add "Ka'asher Tzivah Hashem es Moshe" here and by the termination of each subsequent Melachah that the workers performed?
Seforno (in Pasuk 5): To teach us that, by each and every Melachah that they performed, they had in mind to carry out the will of Hashem as He commanded Moshe. 1
Ayeles ha'Shachar: To teach us that, in spite of the difficulty in fulfilling every minute as per instructions, they did everything correctly, without the slightest deviation.
Oznayim la'Torah: To make up for the fact that, at Moshe's own request, his name is missing from the whole of Parshas Tetzaveh - the Parshah which first discusses the Bigdei Kehunah), the Torah repeats "Ka'asher Tzivah Hashem es Moshe" whever it discusses the making of the Bigdei Kehunah 2 - both here and in Tzav. 3
Yerushalmi B'rachos, 4:3: The eighteen B'rachos that comprise the weekday Amidah correspond to the eighteen times that the phrase "Ka'asher Tzivah Hashem es Moshe" appears in Pikudei.
Ba'al ha'Turim: Refer to 40:21:1:1.
Yerushalmi (Ibid.): Not counting the first time. See Torah Temimah, note 3. Refer also to 40:21:1:1.
See also Oznayim la'Torah who elaborates further and who refers to the Ba'al ha'Turim at the end of the Parshah.
Perhaps we can add that for same reason, in Tetzaveh itself, the Torah begins Parshah after Parshah, with the word "ve'Atah" to stress that although Moshe's name is not mentioned, nothing is done outside his authority.
