I should also add that there is also some dispute concerning sources.
The only available near-contemporary source we have are the gospels themselves, which provide Semitic snippets in the form of proper names (Golgotha, Gethsemane, Bartholomaios, Barabbas, Bariōnas, Boanērges, Kēphas, Thōmas, etc.), words (hōsanna, korban, raka) and short phrases (Abba; Talitha kum; Ephphatha; Maranatha; Eloi Eloi lema sabachthani). Some of these are Aramaic, while others are Hebrew, and still others could be either. Determining the specific language of these loanwords is at times difficult not only because Aramaic and Hebrew are closely related (both are Semitic languages), but also by the fact that the spoken Hebrew of Jesus’ time is believed to have been Mishnaic Hebrew - a variety heavily influenced by Aramaic, which incorporated a large amount of Aramaic loans. Not to mention the fact that when the text itself refers to the language of such Semitic glosses, it applies to it terms like “Hebrew,” even if the gloss in question is more likely to be Aramaic rather than the language we call ‘Hebrew’ today. And there is also no guarantee that the Aramaic snippets were transmitted in the original Galilean dialect rather than in, say, Judaean Aramaic.
No literary source transmitting the idiomatic and colloquial language spoken in the Galilee at the time of Jesus is available. Very few Aramaic writings of any description survive from that period and not a single piece represents the dialect of the Galilee. While some like Fr. Joseph Fitzmyer have a stricter view, thinking that only contemporary sources (such as the Aramaic attested at Qumran) provides valid comparative material, others like Geza Vermes and Maurice Casey are willing to take into consideration the so-called ‘Galilean Aramaic’ attested in later rabbinic literature and Syriac translations like the Peshitta.