In terms of how true it is, the introduction to the Midrash purports that it was found by a Roman officer in the ruins of Jerusalem in 70. This would mean it is from the Second Temple Period (or earlier). That does not seem to be the case. According to Wikipedia:
Scholars have proposed various dates between the 9th century and 16th century.
Prof. Joseph Dan is of the opinion, that the work was written in Naples in the early sixteenth century. (See here)
Similarly, Avi Margolis accepts the 16th century date.
Nevertheless, it could be claimed (see here) that that introduction was added when they printed the work in the 17th century (possibly based on a 16th century edition), but that earlier versions didn't make this claim.
In terms of authoritativeness, it could theoretically still be from a legitimate (albeit unknown) source in the Geonic period or later, who simply chose to present it as an earlier work, in which case it would be at most as authoritative as other post Talmudic Midrashim.
Indeed, some (see Hida below) assume that this Midrash is that referred to as "Sefer Milhamot B'nei Yaakov" by Ramban (Genesis 34:23) and Rabbenu Bahye (Genesis 35:6). Their citation would indicate a degree of legitimacy to the work. However, while Rabbenu Bahye quotes it without reservation, Ramban adds the caveat "if we believe in the book Milhamot B'nei Yaakov":
אם נאמין בספר מלחמות בני יעקב
R. Yehuda Aryeh de Modena of Venice criticised the work as a forgery and removed its claims of antiquity (see here).
Hida in Shem Hag'dolim (Maarekhet HaSefarim: Yashar) writes that many do not believe in this work, notes that Rabbenu Bahye apparently did, and that Ramban was unsure.
More recently, R. Avraham Mordekhai Albert wrote here that the work is not an ancient Midrash, but a mere compendium of Midrashim. He seems to attach no importance to it as an independent work.
It is important to note that, even the Midrashim of Hazal are not necessarily true.