I am by far no expert on the field, but I know enough to answer the linguistic and cultural aspect of the cosmopolitan nature of Jerusalem around 1 AD. Jerusalem and the region of Palestine had experienced a number of foreign invasion in the centuries before 1 AD, which led to a number of languages being spoken in the region. Most people would speak Aramaic, a language in the Semitic language family, which most believe a person like Jesus would have spoken. There was also a Hellenised elite that spoke Koine Greek. This was result of the establishment of the Hellenistic world by Alexander the Great some 300 years previously after he conquered the Levant, Egypt and Persia, which led to the local elites in the region adopting Greek and Greek culture, something which also happened with the Jews living in Jerusalem and Palestine. Lastly, Palestine and thus Jerusalem was controlled by the Roman Empire around 1 AD, so you would also have a ruling elite that spoke Latin. So, in short, Jerusalem would be quite cosmopolitan when considering the different languages and cultures of the people that inhabited the city.
Those are two questions that take the discussion in different directions. The short answer to the first: Fairly cosmopolitan, in the sense that it was a pretty thriving economic center, due, at least in part, by religious tourism that cropped up before, during, and after the time of Jesus. It turns out that the temple built by Herod the Great had a reputation all throughout the empire, which drew Gentile travelers. Their interest would be part sight-seeing and part religious (Crossan, in "God and Empire," claims that Judaism would have grown in converts quite a bit if it weren't for the requirement of circumcision). Roughly around the time Jesus, Jerusalem also saw an influx of inhabitants, which meant both more wealth and social conflict that can result - this will be a huge problem in a few minutes.
Ethnically, it was almost entirely Jewish (bracketing out the disagreement over the label of Jew/Judean), and during the festivals, Jews from throughout the empire, and especially Galilee, would cause the city to swell quite a bit. There would be a small percentage of Samaritans and miscellaneous Gentiles living there as well, but I'm not aware of any research that has given convincing, definitive numbers. Rome also had a presence, and they were most visible during certain festivals like Passover, where nationalism had a tendency to bubble up and erupt into riot. Pontius Pilate, for example, would move his headquarters from Caesarea to the fortress of Antonia which overlooked the Temple Mount during times of potential unrest (again, eg, Passover).
Aside from Roman Rule, who had varying degrees of direct interaction, the biggest cultural/social/political force was the temple (as a rule, in ancient jewish culture, there really is no distinction between culture, religion, and politics). This gave the priesthood a tremendous amount of power and wealth. The office of the High Priest had to be approved by the Romans, a move that allowed Rome to keep the people in check to at least some extent. The temple itself was the central cultic force for Judaism (although Torah as its center was growing rapidly at this time, due to an emerging sense of ambiguity toward the temple and its priests, along with the synagogue). The priests and Sanhedrin formed the basis of the ruling class, at least from a local perspective, and from a modern perspective, we would say that much of this power was derived from its religious and economic influence.
Josephus mentions that at the outbreak of the war in 66CE, once the rebels took the portion of Jerusalem that contained the temple, they burned the debt records that were kept at the temple. This alone gives us a picture of how the society was organized. The temple was an important economic and religious center, with the priests (and especially the high priest) in close proximity to this wealth and power. Discontentment was rapidly growing due to very poorly distributed wealth, and we can say that wealthy elite floated to the top and were above a large and growing number of poor.
Hopefully this helps. Let me know if that doesn't get at what you wanted to know. Here are a few sources for followup:
Goodman, Martin: "The ruling class of Judaea: the origins of the Jewish revolt against Rome, A.D. 66 - 70" Perrin, Nicholas: "Jesus the Temple" Sanders, EP: "Judaism: practice and belief, 63 BCE-66 CE" Horsley and Hanson: "Bandits, prophets, and messiahs: popular movements in the time of Jesus"