Some strange, controversial, or non-halakhic content is the following:
- The Targum to Genesis (21:21) lists Yishmael's wives as Adisha and Fatima. Fatima was the wife of Ali and Aisha was the wife of Mohammed. This parallel to Yishmael is striking.
- Numbers (24:19) mentions Constantinople. This seems anachronistic for an allegedly Tannaic Targum.
- Leviticus (7:27) could be interpreted as forbidding the consumption of the blood of fish.
- Numbers (5:17) suggests a vessel is necessary to take water from the kiyyor. This is not found in halakha.
- Leviticus (18:21) presents a biblical prohibition against impregnating a non-Jewish woman, instead of for molekh; an interpretation condemned by the Mishna Megilla (4:9). Notably, this interpretation was popular among Karaites.[i]
- Leviticus (1:4) and (3:2) indicates that semikha must be done with the right hand in particular. Notably, this too was a Karaite position.[i]
- Deuteronomy (34:5) indicates that the exemption for a newlywed groom from going to battle, only applies to marriage to a virgin. This was also the position of many Karaites.[i]
- Leviticus (19:20) indicates that the shifha harufa is betrothed to a free man. According to halakha, the betrothal is to a slave (Sifra Kedoshim 5:2).
- Exodus (22:2) indicates slaves are freed at shemitta; not after seven years.
- Deuteronomy (22:5) indicates that shaving the face is lo tilbash. This is not mentioned in classical halakhic sources (yes I know the Tsemah Tsedek).
- Leviticus (13:45) has a herald shouting tamei tamei, rather than himself. This halakha is not found elsewhere.
- Exodus (12:46) introduces a prohibition of giving gifts on Pesah.
- Leviticus (11:11) bans benefit from non-kosher fish.[ii]
- Deuteronomy (22:26) could be read as requiring a get from the rapist of a naara m'urasa. This is against halakha as she couldn't become mekudeshet to him anyway (and there is no reason to assume that she did even if she could).[iii]
- Numbers (18:13) indicates that bikkurim is brought from all fruit trees; not just the seven species, but apparently not wheat or barley which are included in the seven.
- Leviticus (22:28) emphasises that the reason for the prohibition of slaughtering a cow and its calf on the same day is mercy. This is against the Yerushalmi Berakhot (5:3) that opposes such a Targum:
לא עבדין טבות שעושין למדותיו של הקב"ה רחמים ואילין דמתרגמין עמי בני ישראל כמה דאנא רחמן בשמים כך תהוון רחמנין בארעא תורתא או רחילה יתה וית ברה לא תיכסון תרויהון ביומא חד לא עבדין טבאות שהן עושין מדותיו של הקב"ה רחמים
Compare that to the wording of the Targum:
עַמִי בְּנֵי יִשְׂרָאֵל הֵיכְמָא דְאָבוּנָן רַחֲמָן בִּשְׁמַיָא כֵּן תֶּהֱוֹן רַחֲמָנִין בְּאַרְעָא תּוֹרָתָא אוֹ רְחֵילָא יָתָהּ וְיַת בְּרָהּ לָא תִיכְסוּן בְּיוֹמָא חָד
Presenting the very banned Targum certainly raises eyebrows.[iv]
[i] See The Jewish Quarterly Review, Volume 2 pp. 536-7. Notably Geiger noted some other overlap between Targum Pseudo Jonathan and Karaite interpretation, as noted in JQR there.
[ii] Although Sifra Shemini (3:11) bans trade with forbidden fish, although allows benefit generally.
[iii] Alternatively this could be read as requiring the betrother to divorce her. This would be related to the view of Avuha Dishmuel in Ketubot (51b) that a raped woman is forbidden to her husband since she might have acquiesced. It is certainly not the halakha though, and Avuha Dishmuel himself did not defend his position against seeming refutation.
[iv] Seeing other commentators (e.g. Moreh Nevokhim 3:48) suggest that the reason is divine mercy might also raise eyebrows, but that doesn't resolve the issue with the Targum; it just leaves two issues. In reality, the problem with the Targum is greater since some things may be appropriate to say, but not in the context of a Targum. For example, Megilla (4:10) states that some verses are not to be translated (by the meturgeman) at all. The Mishna clearly didn't ban the study or discussion of these verses, but their presentation in a Targum format. Similarly, a ban on a certain Targum may be limited to a Targum format, rather than simply explicating the idea.
Culled from this dissertation.