I'll try to answer this question by quoting from Tov, E. (2001). Textual criticism of the Hebrew Bible. (2nd ed.). Minneapolis: Augsberg Fortress. In Tov's words:
The Septuagint is a Jewish translation which was made mainly in Alexandria. Its Hebrew source differed greatly from the other textual witnesses (the Masoretic text, the Targumim, the Peshitta, the Vulgate, and many of the Qumran texts)... [It] is important as a source for early exegesis, and this translation also forms the basis for many elements in the New Testament. (p. 134)
So according to Tov, the Septuagint (or at least the core part) was a Jewish translation, though the text it was based on differed from the Masoretic text in some places. It was later used by the Christians for their own agendas, but this does not mean that it had a non-Jewish agenda originally.
The Septuagint is known in various languages as the translation of the seventy (two elders). Its traditional name reflects the tradition that seventy two elders translated the Torah into Greek... In the first centuries CE this tradition was expanded to include all of the translated biblical books, and finally it encompassed all of the Jewish-Greek scriptures...
According to the generally accepted explanation of the testimony of the Epistle of Aristea, a translation of the Torah was carried out in the third century BCE... The translation of the books of the Prophets, Hagiographa, and apocryphal books came after that of the Torah, for most of these translations use its vocabulary, and quotations from the translation of the Torah appear in the Greek translations of the Latter Prophets, Psalms, Ben Sira, etc. Since the Prophets and several of the books of the Hagiographa were known in their Greek version to the grandson of Ben Sira at the end of the second century BCE, we may infer that most of the books of the Prophets and Hagiographa were translated in the beginning of [the second century BCE] or somewhat earlier...
[The Septuagint] also contains revisions (recensions) of original translations. These revisions were made from the first century BCE onwards until the beginning of the second century CE. (pp. 136–137)
So the later sections of the Septuagint did indeed have different authors from the original translation of the Torah, but they were all authored before the advent of Christianity, and apparently used by Jews. Later on some versions of the Septuagint were revised, and some of these revisions were after Christianity was born. Tov explains elsewhere that some of these revisions were clearly Jewish; for example, the revision of Aquila (who might have been the famous Onkelos) was used in synagogues until the sixth century CE. Other recensions were authored by Christians, e.g. that of Lucian of Antioch in 312 CE.
What can we say about the versions of the Septuagint used today? There exist academic editions known as critical editions which try to reconstruct the original text free of the influence of later recensions; I infer that these are unlikely to contain Christian influence, since the pre-revision text of the Septuagint was Jewish. As for the version used by the Greek Orthodox Church, I am not sure to what extent it is affected by Christian recensions, or whether they would contain any objectionable ideological intrusions in the first place. In any case, it seems to me that if one wanted to consider the Septuagint in a Jewish context, it would be most appropriate to use a critical edition so as to avoid foreign influence.
As to whether the translation is "reliable" -- I'm not sure what that term means or how to evaluate it, besides knowing that the Septuagint was originally written and used by Jews. It does seem natural that Jews became less comfortable with it after it was appropriated by the Christians. As Tov explains:
The first Christians quite naturally chose the Septuagint as their Holy Writ and as the source for additional writings since Greek was their language. As a result, [it] influenced them not only by the content of the translation in general, but also by its terminology. The frequent use of the Septuagint by the Christians caused the Jews to dissociate themselves from it and to initiate new translations. (p. 143)
Of course, there are texts such as Ben Sira that were written by Jews in the pre-Christian era that we do not accept as canon, so perhaps the Septuagint should have a similar status: interesting and potentially valuable, but not infallible. Also, keep in mind that we do often use the Targum Yerushalmi, despite the fact that it has plenty of "translations" which clash with the other traditional sources. But in any case, my speculation about how we should view the Septuagint is just that -- speculation.
In summary, I don't see a reason to be suspicious of the Septuagint itself, as long as one reads it in a Jewish context without the "baggage" that Christians come to the table with, and uses a critical edition or the recension of Aquilas (or some other Jewish recension). However, I can't say how much regard it should be given either.