The episode of the midwives saving the Hebrew babies from infanticide is missing in Jubilees, and rather than Jochebed keeping Moses three months until she could no longer hide him, and then putting him in a basket on the Nile, in Jubilees she does this every day until after three months, Pharaoh's daughter notices it.
Pharaoh's daughter, as I have remarked before, is not named in the Bible. The Midrash names her Batyā, but Josephus, writing several centuries before the Midrash was written, gives her the name Thermutis. Jubilees, written two and a half to three centuries before Josephus, concurs, naming her Tharmuth. (The story in Josephus of Moses leading the war against the Nubians is missing here, though.)
After Pharaoh's daughter discovers the baby, the Bible describes how Miriam manages to get Moses' own mother to act as paid wet-nurse for him. Jubilees adds to that Amram teaching him to read and write. (I'd love to know whether the author expected that to be in the Hebrew alphabet or hieroglyphics and demotic, but sadly the author does not tell us that.)
In the Bible, Moses flees into exile after killing an Egyptian who was beating a Hebrew, "from his brethren"; in Jubilees the Hebrew man is specifically referred to as Moses' friend; maybe the author didn't feel ties of ethnicity were enough to motivate him to act?
Chapter 48There's a strange incident in Exodus 4:24-26 which reads:
Jubilees, uncomfortable with the implication that God tried to kill Moses, changes this to Prince Mastema (Satan):
It came to pass by the way in the inn, that the Lord met [Moses], and sought to kill him. Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, "Surely a bridegroom of blood are you to me." So he let him go: then she said, "A bridegroom of blood you are," because of the circumcision. וַיְהִי בַדֶּרֶךְ בַּמָּלוֹן וַיִּפְגְּשֵׁהוּ ה׳ וַיְבַקֵּשׁ הֲמִיתוֹ׃ וַתִּקַּח צִפֹּרָה צֹר וַתִּכְרֹת אֶת־עָרְלַת בְּנָהּ וַתַּגַּע לְרַגְלָיו וַתֹּאמֶר כִּי חֲתַן־דָּמִים אַתָּה לִי׃ וַיִּרֶף מִמֶּנּוּ אָז אָמְרָה חֲתַן דָּמִים לַמּוּלֹת׃
You yourself [Moses] know what He spoke to you on Mount Sinai, and what prince Mastema desired to do with you when you were returning to Egypt. Did he not with all his power seek to slay you and deliver the Egyptians out of your hand when he saw that you were sent to execute judgment and vengeance on the Egyptians? I [the Angel of the Presence] delivered you out of his hand.