While a number of Jewish commentaries have been written on Targum Onkelos, Targum Yonasan, Targum Pseudo-Yonasan, and Targum Yerushalmi (see the list in the Targum section at Parshablog, for example), have there been any Jewish commentaries authored on the Targum Shiv'im, (a.k.a. the LXX or Septuagint)? If so, where can I find them (or, if only one has been written, where can I find it)?
There is a current academic attempt (by Prof. Moshe Tzipor from the Bar Ilan University) to reconstruct the original Hebrew text the Greek translation was based on. It has extensive notes, comments and explanations. As far as I can tell, only the first volume (Bereshit/Genesis) has been published so far:
Nearly all of Philo's writings are explanations of the Septuagint version of the Pentateuch, though I believe the only ones that actually go through the books in order as a commentary are his Questions and Answers on Genesis (at the above link) and Questions and Answers on Exodus.
Other Jewish authors who used the Septuagint, such as Artapanus, Ezekiel and Demetrius, are only known to us from quotations from Eusebius and Clement of Alexandria (the respective Wikipedia pages give the exact references). However, they often give paraphrases or embellishments (sometimes only loosely based on the text), rather than commenting directly.
R. Hayim Heller wrote a sefer on the Septuagint. I'm not sure if you would quite call it a commentary, but you can access the sefer here. I think he also wrote something on it in German, called Untersuchungen zur Septuaginta. As described in his profile page on YUTorah:
A gaon in Mikra, he published the Targum HaPshitah on Bereishit and Shemot and a German language work on the Septuagint.
The late Harry M. Orlinsky was an expert on the LXX. While he wrote no commentary on the whole translation, he did publish important articles on it. A Google search ('Harry Orlinsky on the Septuagint') will reveal his work in this field. He earned his doctorate from Dropsie College for his work on the translation of Job in the Septuagint. He also studied the anthropomorhisms and anthropopathisms as treated in the translation of Isaiah. And he wrote an essay entitled 'The Hebrew Vorlage of the Septuagint of the Book of Joshua.' See further 'The Septuagint: the Oldest Translation' in his book Essays in Biblical Culture and Translation (Ktav, 1974). Orlinsky was co-founder and first president of The International Organization for Septuagint and Cognate Studies.
For the general need of such a commentary, see 'Prospective for a Commentary on the Septuagint Sponsored by The International Organization for Septuagint and Cognate Studies' (ccat.sas.upenn.edu/ioscs/commentary/prospectus.html). The Society of Biblical Literature embarked on producing such a commentary in conjunction with IOSCS in 2005, and it now stands at thirteen voumes (as of 2015) and is published by Brill (https://www.logos.com/.../septuagint-commentary-series).
Though initial Jewish reaction to the LXX was positive (see Philo), later Jewish sentiment was negative.
“Seventy elders wrote the entire Torah for King Ptolemy in Greek, and that day was as difficult for Israel as the day it made the [Golden] Calf, for the Torah could not be properly translated” (Masekhet Soferim 1:7).
“Rabbi Yehuda La-Levi ben Rabbi Shalom said: Moshe wanted the Mishnah to be written as well, but the Holy One foresaw that the nations of the world would translate the Torah, read it in Greek, and say ‘We, too, are Israel’” (Tanḥuma Vayera 6).
This negative sentiment manisfests itself in the fact that no commentary on the LXX has ever been written in Judaism. The translations of Aquila and Theodotion, the next closest thing to commentaries on it, were suppressed eventually and are no longer extant.