So the Mishna and Gemara
are books on religious controversies, and those issues were solved through debate within them. Considering how Judaism views earlier 'cases' of rabbinic law to have precedence over later decisions, any early changes impact the future outlook of the entire religion. Even further changes are possible since the Jews have a kingdom in Israel, and will presumably be building the temple and re-instituting the Sanhedrin, which will allow them to change religious law as seen fit.
Honestly the time of the Mishna and Gemmara constituted a period where every aspect of religious life was up for grabs, and the rabbbi's made a series of decisions based on what aspects of Judaism should change after the destruction of the temple. To quote wikipedia:
"After the
Bar Kochba Revolt, Rabbinic scholars gathered in
Tiberias and
Safed to re-assemble and re-assess Judaism, its laws, theology, liturgy, beliefs and leadership structure. In 219 CE, the
Sura Academy (from which
Jewish Kalam emerged many centuries later) was founded by
Abba Arika. For the next five centuries, Talmudic academies focused upon reconstituting Judaism and little, if any, philosophic investigation was pursued."
Traditionally the decisions in the Talmud have a "most stringent, and a "least stringent" opinions in their text, or debate will continue until they reach a majority consensus on an issue. Sometimes they made certain areas of Jewish observance much more stringent then they actually were, like outlawing mixing poultry and dairy even though poultry wasn't considered meat at the time, or deciding that certain laws (the ones calling for people to be stoned to death for trivial matters), were ridiculous (they literally say that none of them have ever seen it happen ever, except for one rabbi that says that his friend saw the grave of a person killed by stoning once), and enacting legalistic religious restrictions to ensure they didn't happen.
So really, changes are probably fine as long as they mesh with the culture and ethics of Jewish society. But to give you some examples of potential things you could use:
There's the split of Karaite Judaism from the mainstream, rejecting the Mishna and Gemmara, and the validity of rabbinic law in general. Probably the biggest split.
There is going to be conflict over beliefs of the remaining theologies from the 2nd Temple period, some of which should still be around.
Probably religious conflict or crossover between Samaritans and Jews of some kind.
Judaism's opinions on Christianity as a movement, ie. are they still part of Judaism.
The books of the Tanakh were supposedly canonized in the 2nd Century, but you could probably add more at this point and have them be contentious.
The degree to which Jews should integrate into societies and interact with the outside world, status of Kosher laws, etc. Whether or not intermarriage is allowed, considering the bible only says not to marry Cannanites, which technically doesn't exclude everyone else.
There's the decision to make Judaism matriarchal instead of patriarchal, having the official status as "a jew" pass down through the mother rather than the father. Really the debate of "who is a jew" that allows people to convert or not. There was still some resentment on converts who 'de-converted' immediately after the Roman's destroyed the temple.
The role that sacrifice should play in the religion, and if it should be replaced entirely by prayer. Should sacrifice resume if the temple is rebuilt?
The status of 'secular' ie. Greek philosophies in accordance to Judaism. Is studying these beliefs heretical? Issues with Gnostic religious practices. There were especially factions that denounced the philosopher Epicurus.
https://en.wikipedia.org/wiki/Epikoros
Actually, the exact definition of heresy is codified in the mishna, so you could conceivably change that if you wanted.
The debates between the House of Hillel and House of Shammai. (two schools of though on different practices and rituals within Judaism)
https://en.wikipedia.org/wiki/Hillel_and_Shammai
Debate over whether or not the lost tribes will return to Israel, and whether one should search for them.
The role of capital punishment in Judaism
Debate over whether polygamy is permissible or not.
Whether or not the rulings of non-Jewish courts are valid.
Degree of ritual purity required for everyday religious life.
What constitutes breaking the Sabbath, when you are allowed to break the Sabbath.
Here are some wikipedia links that may help:
https://en.wikipedia.org/wiki/Takkanah
https://en.wikipedia.org/wiki/Jewish_schisms
https://en.wikipedia.org/wiki/Jewish_religious_movements
https://en.wikipedia.org/wiki/Jewish_philosophy