Gemara

(Rav): Anyone who says an unnecessary Berachah transgresses "Lo Sisa (Es Shem Hash-m Elokecha la'Shav)."

Nedarim 7b (Rav): If David hears Reuven say Hash-m's Name in vain, he must excommunicate Reuven. If he does not, he should be excommunicated.

Menachos 36a (Rav Chisda): If one talked in between (putting on the Tefilin Shel Yad and the Shel Rosh), he blesses again.

Inference: If he did not talk, he does not bless again.

Question: R. Chiya brei d'Rav Huna taught that we bless 'Lehani'ach Tefilin' on the Shel Yad, and 'Al Mitzvas Tefilin' on the Shel Rosh!

Answer (Abaye and Rava): If he talked, he blesses twice. If he did not talk, he blesses once.

(Beraisa): If one talked in between the two Tefilin, this is an Aveirah that disqualifies him from fighting in war.

Berachos 60b: When putting Tefilin on his arm, one blesses "Asher Kidshanu... Lehani'ach Tefilin." When putting Tefilin on his head, he blesses "Asher Kidshanu... Al Mitzvas Tefilin."

Rishonim

Rambam (Hilchos Tefilin 4:5): One who puts on both Tefilin blesses once, 'Lehani'ach Tefilin.'

Rambam (Hilchos Berachos 1:15): If one blesses unnecessarily, he says Shem Shamayim l'Vatalah. One may not answer Amen after him.

Rambam (4:10) If one blesses on a food and it fell and was burned, he says 'Baruch Shem Kevod...' lest his Berachah be Shem Shamayim l'Vatalah.

Rambam (Hilchos Shevu'os 12:11): If one said His name l'Vatalah, he should rush to praise and glorify His name, lest the mention be l'Vatalah. He says 'Baruch Shem...' or 'Gadol Hu u'Mehulal Me'od' or something similar.

Rosh (Berachos 6:20): If one said a Berachah l'Vatalah, he says Baruch Shem Kavod.... If he only said Baruch Atah Hash-m, he finishes Lamdeni Chukecha, to avoid a Berachah l'Vatalah.

Question: How can one excommunicate one who said Shem Shamayim l'Vatalah? Perhaps he said Baruch Shem..., and fixed his transgression!

Answer (Einayim l'Mishpat, ibid.): Perhaps Baruch Shem... does not fix the transgression. It is merely Teshuvah. Tosfos (Berachos 39a DH Botzar) holds that it helps only for a Berachah l'Vatalah (which is not mid'Oraisa). The Rambam holds that it helps only if he was Shogeg.

Rosh (Kidushin 1:49): R. Tam says that women may bless on a Mitzvas Aseh sheha'Zeman Gerama. Even though they are exempt even mid'Rabanan, since they intend for a Berachah, it is not Lo Sisa.

Rosh (Hilchos Tefilin 14): Rashi explains that if one did not talk, he blesses only Lehani'ach Tefilin. If he talked, he blesses also Al Mitzvas Tefilin on the Shel Rosh. R. Tam and Shimushah Raba explain that if he did not talk, he blesses once on the Shel Rosh, i.e. Al Mitzvas Tefilin, its proper Berachah. If one talked, he blesses twice on the Shel Rosh, Lehani'ach Tefilin and Al Mitzvas Tefilin. It seems that this is correct. If the Berachah Al Mitzvas Tefilin was enacted for the Shel Rosh when he puts it on alone, why shouldn't one bless it also when he wears the Shel Yad? If Lehani'ach Tefilin exempts both of them, one should say the same Berachah on the Shel Rosh alone! Why was another Berachah enacted? Rather, it was enacted to bless Lehani'ach Tefilin, and this applies also to the Shel Rosh. When he puts on the Shel Rosh, he blesses also Al Mitzvas Tefilin, for this completes the Mitzvah. Therefore, if he talked and was Mesi'ach ha'Da'as (diverted his mind), he must bless again Lehani'ach Tefilin. Also, 'Chozer u'Mevarech' connotes that he repeats the Berachah that he already said. However, the questioner thought that it means that he blesses a new Berachah. Most Ge'onim say to say two Berachos. In my youth I used to bless once. My brother heard so from R. Shmuel of Ivra, since Rabanan argue about this and the Berachos are not Me'akev the Mitzvah. The Gemara connotes that one blesses twice, and so did Maharam me'Rotenburg.

Ran (Rosh Hashanah 11a DH Sha'alu, citing Ba'al ha'Ma'or 12a): Talking in between the two Tefilin is an Aveirah, because even though they are two Mitzvos, one must not separate between them. If he separated, he must bless again on the Shel Yad, tighten the knot, and bless a second Berachah on the Shel Rosh.

Tosfos (Rosh Hashanah 33a DH Ha): The Gemara (Temurah 3b) expounded that Shem Shamayim l'Vatalah is forbidden (mid'Oraisa). This does not apply when it was in an (invalid) Berachah.

Magen Avraham (OC 215:6): One who says an unnecessary blessing transgresses "Lo Sisa" (Berachos 33a). Tosfos (Rosh Hashanah 33a DH Ha) and the Rosh (Kidushin 1:49) hold that this is mid'Rabanan. The verse is merely an Asmachta. The Rambam holds that it is mid'Oraisa.

Eshel Avraham (Ofenheim): The Rambam agrees that it is only mid'Rabanan, unlike the Magen Avraham.

Poskim

Shulchan Aruch (OC 25:5): One says one Berachah, Lehani'ach Tefilin, on both Tefilin.

Beis Yosef (DH va'Yevarech): Rashi explains that if one talked in between, he blesses twice. If he did not talk, he blesses only on the Shel Yad. It seems that the Rif and Rambam agree. Semag says that he found in the Medrash Yelamdenu like R. Tam. Even though the Yerushalmi (says unlike this), the Bavli is primary.

Beis Yosef (DH veha'Agur, citing the Agur): The Zohar says to bless only once. If Rabanan saw this, why do they argue with R. Shimon?! In any case, the custom is to bless twice.

Beis Yosef (ibid.): Why was the Agur more surprised by this, than other laws in which Poskim rule like the Gemara, unlike the Zohar? The Zohar was not known in the days of the Poskim. Also, it is not clear that the Zohar says to bless only once. Mahari Ben Chaviv used to bless twice, and after the second Berachah he would say Baruch Shem... to save himself from a Safek Berachah l'Vatalah. I say that one should not bring himself to a Safek Berachah l'Vatalah and rely on saying Baruch Shem....! We hold like the Rif and Rambam, especially since Rashi and the Rashba agree. This is the custom, to bless only once.

Rema: Some say that one blesses Al Mitzvas Tefilin on the Tefilin Shel Rosh even if he did not talk in between. This is the custom of Ashkenazim.

Magen Avraham (9): We bless Al Mitzvas Tefilin (singular), for it refers only to the Shel Rosh. Even according to the Tur, who says that it applies also to the Shel Yad, I bless Mitzvas, for both are like one. Divrei Chamudos (Hilchos Tefilin 55) says so. Also, Mitzvas can refer to Mitzvos, like it says "Mitzvas Hash-m Barah", but Mitzvos cannot refer to one Mitzvah.

Gra (DH v'Yesh): The opinion of Rashi, the Rif and Rambam is primary. The Tosefta (Berachos 6:15) says 'when he puts them on, he blesses Lehani'ach Tefilin.' Another Tosefta (6:19) says that if one was about to separate Terumah and Ma'aseros, he says one Berachah. If he talked in between, he blesses the Berachah proper for each. The Rambam, Tur and Shulchan Aruch (YD 331:78) rule like this. The Rema did not comment. One Berachah suffices for different Mitzvos with different names, if he did not interrupt. Also, if one interrupted, how can he say two Berachos on the Shel Rosh, since he is still wearing the Shel Yad? Similarly, if one has only the Shel Rosh, how can he say twice "v'Tzivanu" on one Mitzvah? Why is this different than several Talesim with Tzitzis? If he wears them at once without an interruption, he bless only once (OC 8:12).

Aruch ha'Shulchan (10): Berachos 60b connotes that [always] one must say two Berachos on the Tefilin.

Rema: It is good to always say after the second Berachah Baruch Shem....

Eshel Avraham (10): The Levush omitted Baruch Shem.... Eliyahu Rabah (9) says that R. Tam's opinion is primary; we say Baruch Shem... l'Ravcha d'Milsa (to justify the Berachah according to all opinions). It is not clear whether one may answer Amen if he hears another bless Al Mitzvas Tefilin, for we do not answer Amen to a Berachah l'Vatalah.

Kitzur Shulchan Aruch (10:4): One says Baruch Shem Kevod because there is a little Safek of a Berachah l'Vatalah. Therefore, it is a Safek whether one should answer Amen. Therefore, it is good to say the Berachah quietly (lest others hear it).

Mishnah Berurah (21): It is not really a Safek Berachah l'Vatalah. If so we would not bless and rely on Baruch Shem...! Rather, we Ashkenazim hold that the Halachah follows R. Tam. The custom is to say Baruch Shem.... l'Ravcha d'Milsa. One must be careful not to say it before properly tightening the Shel Rosh. If not, Baruch Shem... interrupts between the Berachah and the wearing, and the Berachah is Vadai l'Vatalah, and he must bless again. People stumble in this!

Kaf ha'Chayim (40): If one hears another bless '...Al Mitzvas Tefilin', he answers Amen in his heart.

Halichos Shlomo (4:19(27)): If one hears it, he must answer Amen. It was enacted to bless mi'Safek and say Baruch Shem..., for this is better than wearing the head Tefilin without a Brachah.

She'elas Rav (ha'Gaon R. C. Kanievsky Shlita, 2:19:27): One may answer Amen to a Safek Berachah l'Vatalah, but it is not obligatory.

She'elas Rav (2:2:20). According to the letter of the law, one need not say Baruch Shem Kevod... at all, therefore one may answer Amen [or to Kaddish] before saying it.

Kaf ha'Chayim (36): One of the questions they asked Shamayim was whether the Halachah follows the Rif (R. Yitzchak Alfasi) and the Ge'onim with him. The answer was "Es Brisi Akim Es Yitzchak." The Ari Zal holds like this.

Bi'ur Halachah (DH v'Tov): R. Akiva Eiger advises to intend 'if the Halachah requires only one Brachah on Tefilin, my first Brachah does not exempt the head Tefilin.' It is as if he talked in the middle, so he may bless on the Shel Rosh even according to Rashi. This is not causing an unnecessary Brachah, for he must do so due to the Safek about the Halachah, and other reasons. Also others suggested this. The Pri Megadim concludes not to do so. One should not accustom himself to question customs of Yisrael based on many Rishonim.