The halacha we have today is mostly sourced in Talmud Bavli(the Babylonian Talmud),Medrash and Zohar. I would like to know what Halachot in which we rule according to the Yerushalmi (the Jerusalem Talmud) versus the Bavli (the Babylonian Talmud)?
Basar Shenitalem Min Ha'ayin would be an example of this:
The Gemara Bavli in Hullin 95a and 95b, rules that the thing we are worried about is an animal (according to rashi a raven, according to the rambam "a wild animal or vermin" (my rough translation)) switching the meat. The gemara holds that this doesn't apply if it was in the hands of a non-Jew -- meat left with a non-Jew is not considered a problem according to the Bavli.
The Shulchan Aruch (63:1) rules, unlike the gemara referenced above, that we are also worried about non-Jews in terms of basar shenitalem min ha'ayin. The GR"A (S"K 1) says that this is based on the Rambam in Ma'achalot Assurot 8:10, who rules like the Yerushalmi in Shekalim 7:2 ( "כדרכו ברוב מקומות" - "as is his way in most places" - GR"A), NOT like the Bavli I quoted above.
Tosfot in Menachot 33b sv. U'mai quotes a Yerushalmi that he says argues on the Bavli regarding how high to put a mezuzah on an extremely tall doorway. The Bavli rules that it should be in the top third of the doorway regardless, while the Yerushalmi rules that in this case the mezuzah should be hung around shoulder height.
According to Rav Yisroel Belsky (and other sources all quoted here, footnote 22) the custom follows the Yerushalmi.
According to Rabbi David Bar Hayim, and Rabbi Yehoshua Buch and Rav Chaim Wasserman, whenever the Yerushalmi and Bavli contradict eachother, Jews today living in Israel, should follow the Yerushalmi. The three of them have set up a Beit Din to make such a position on specific customs official, and hallachically legally binding to those who accept the beit din.
Since Jews living in Israel and who feel the beginnings of Geulah no longer live or feel as if they live in Galut, then Jewish practice must follow that of Geulah Judaism and follow in the ways of Israel, instead of the Bavli, which was constructed and recorded for Galut Judaism.
The full practical implications of this view can be found at the machon shilo website.