When Moses' father-in-law Jethro comes to visit him, he sees Moses sitting judging legal cases all day long, and tells him he's going to wear himself out. In Deuteronomy, when Moses is talking about this time, he says:
Deuteronomy 1:9-1:18 דברים א ט-א יח I spoke unto you at that time, saying, "I am not able to bear you myself alone: The Lord your God has multiplied you, and, behold, you are this day as the stars of heaven for multitude. (The Lord God of your fathers make you a thousand times so many more as you are, and bless you, as he has promised you!) How can I myself alone bear your cumbrance, and your burden, and your strife? Take for yourselves wise men, and understanding, and known among your tribes, and I will make them rulers over you." And you answered me, and said, "The thing which you have spoken is good for us to do." So I took the chief of your tribes, wise men, and known, and made them heads over you, captains over thousands, and captains over hundreds, and captains over fifties, and captains over tens, and officers among your tribes. And I charged your judges at that time, saying, Hear the causes between your brethren, and judge righteously between every man and his brother, and the stranger that is with him. You shall not respect persons in judgment; but you shall hear the small as well as the great; you shall not be afraid of the face of man; for the judgment is God's: and the cause that is too hard for you, bring it unto me, and I will hear it. And I commanded you at that time all the things which you should do. וָאֹמַר אֲלֵכֶם בָּעֵת הַהִוא לֵאמֹר לֹא־אוּכַל לְבַדִּי שְׂאֵת אֶתְכֶם׃ ה׳ אֱלֹהֵיכֶם הִרְבָּה אֶתְכֶם וְהִנְּכֶם הַיּוֹם כְּכוֹכְבֵי הַשָּׁמַיִם לָרֹב׃ ה׳ אֱלֹהֵי אֲבוֹתֵכֶם יֹסֵף עֲלֵיכֶם כָּכֶם אֶלֶף פְּעָמִים וִיבָרֵךְ אֶתְכֶם כַּאֲשֶׁר דִּבֶּר לָכֶם׃ אֵיכָה אֶשָּׂא לְבַדִּי טָרְחֲכֶם וּמַשַּׂאֲכֶם וְרִיבְכֶם׃ הָבוּ לָכֶם אֲנָשִׁים חֲכָמִים וּנְבֹנִים וִידֻעִים לְשִׁבְטֵיכֶם וַאֲשִׂימֵם בְּרָאשֵׁיכֶם׃ וַתַּעֲנוּ אֹתִי וַתֹּאמְרוּ טוֹב־הַדָּבָר אֲשֶׁר־דִּבַּרְתָּ לַעֲשׂוֹת׃ וָאֶקַּח אֶת־רָאשֵׁי שִׁבְטֵיכֶם אֲנָשִׁים חֲכָמִים וִידֻעִים וָאֶתֵּן אוֹתָם רָאשִׁים עֲלֵיכֶם שָׂרֵי אֲלָפִים וְשָׂרֵי מֵאוֹת וְשָׂרֵי חֲמִשִּׁים וְשָׂרֵי עֲשָׂרֹת וְשֹׁטְרִים לְשִׁבְטֵיכֶם׃ וָאֲצַוֶּה אֶת־שֹׁפְטֵיכֶם בָּעֵת הַהִוא לֵאמֹר שָׁמֹעַ בֵּין־אֲחֵיכֶם וּשְׁפַטְתֶּם צֶדֶק בֵּין־אִישׁ וּבֵין־אָחִיו וּבֵין גֵּרוֹ׃ לֹא־תַכִּירוּ פָנִים בַּמִּשְׁפָּט כַּקָּטֹן כַּגָּדֹל תִּשְׁמָעוּן לֹא תָגוּרוּ מִפְּנֵי־אִישׁ כִּי הַמִּשְׁפָּט לֵאלֹהִים הוּא וְהַדָּבָר אֲשֶׁר יִקְשֶׁה מִכֶּם תַּקְרִבוּן אֵלַי וּשְׁמַעְתִּיו׃ וָאֲצַוֶּה אֶתְכֶם בָּעֵת הַהִוא אֵת כָּל־הַדְּבָרִים אֲשֶׁר תַּעֲשׂוּן׃
In the Samaritan Torah this passage is interpolated (with appropriate changes of verb tense and person) into Exodus 18:25, thus somewhat reconciling the discrepancy between Exodus and Deuteronomy as to whose idea the devolution of power was, Moses' or Jethro's.
Another famous discrepancy between Exodus and Deuteronomy concerns the commandment to observe the Sabbath in the Ten Commandments. Exodus 19:7 says:
Remember the Sabbath day to sanctify it. זָכוֹר אֶת־יוֹם הַשַּׁבָּת לְקַדְּשׁוֹ׃
Deuteronomy has "Keep the Sabbath day to sanctify it." The traditional Jewish interpreters resolved the contradiction by saying God uttered both words at once; in the Samaritan Torah, however, the text in Exodus reads the same as in Deuteronomy, and there is no contradiction.
There's an addition to the Ten Commandments in both Exodus and Deuteronomy, which is based on Deuteronomy 27:2–8 in the Masoretic text, only with the mountain in question Mt Gerizim, rather than Mt Eval:
It shall be, when He has brought you into the land of the Canaanite which you are coming into, to possess it; you shall set you up great stones, and plaster them with plaster: And you shall write upon them all the words of this law. When you have passed over the Jordan, set up these stones, which I command you this day, on Mount Gerizim. There build an altar to the Lord your God, an altar of stones: do not lift up any iron tool upon them. Build the altar of the Lord your God of whole stones: and you shall offer burnt offerings thereon to the Lord your God: You shall offer peace offerings, and shall eat there, and rejoice before the Lord your God. This mountain is across the Jordan after the way of the sunset in the land of the Canaanite dwelling in the Rift Valley in front of Gilgal by the terebinth of Moreh in front of Shechem. וְהָיָה כִּי־יָבִיאֲךָ אֶל־אֶרֶץ הַכְּנַעֲנִי אֲשֶׁר בָּא שָׁמָה לְרִשְׁתָּהּ׃ וַהֲקֵמֹתָ לְךָ אֲבָנִים גְּדֹלוֹת וְשַׂדְתָּ אֹתָם בַּשִּׂיד וְכָתַבְתָּ עֲלֵיהֶן אֶת־כָּל־דִּבְרֵי הַתּוֹרָה הַזֹּאת בְּעָבְרֶכֶם אֶת־הַיַּרְדֵּן תָּקִימוּ אֶת־הָאֲבָנִים הָאֵלֶּה אֲשֶׁר אָנֹכִי מְצַוֶּה אֶתְכֶם הַיּוֹם בְּהַר גְרִיזִים׃ וּבָנִיתָ שָּׁם מִזְבֵּחַ לַה׳ אֱלֹהֶיךָ מִזְבַּח אֲבָנִים לֹא־תָנִיף עֲלֵיהֶם בַּרְזֶל׃ אֲבָנִים שְׁלֵמוֹת תִּבְנֶה אֶת־מִזְבַּח ה׳ אֱלֹהֶיךָ וְהַעֲלִיתָ עָלָיו עוֹלֹת לַה׳ אֱלֹהֶיךָ׃ וְזָבַחְתָּ שְׁלָמִים וְאָכַלְתָּ שָּׁם וְשָׂמַחְתָּ לִפְנֵי ה׳ אֱלֹהֶיךָ׃ הָהָר הַהוּא בְעֵבֶר הַיַּרְדֵּן אַחֲרֵי דֶרֶךְ מָבוֹא הַשֶּׁמֶשׁ בְּאֶרֶץ הַכְּנַעֲנִי הַיּוֹשֵׁב בְעַרָבָה מוּל הַגִּלְגַל אֶצֶל אֵלוֹן מוֹרֵא מוְּל שְׁכֶם׃
This is significant; it establishes Mt Gerizim as God's chosen place for the Samaritans. As we shall see later on, everywhere that Deuteronomy refers to "the place which God shall choose" to be worshiped, which turned out in Jewish history to be Jerusalem, the Samaritan text reads "the place which God has chosen", and refers to Mt Gerizim, where they still live and worship and sacrifice to this day.Exodus then continues:
The Samaritan text here interpolates the content of Deut. 5:20–23:
Exodus 20:14-15 שמות כ יד-טו And all the people saw the thunderings, and the lightnings, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off. They said to Moses, "You speak with us, and we will hear: but let not God speak with us, lest we die." וְכָל־הָעָם רֹאִים אֶת־הַקּוֹלֹת וְאֶת־הַלַּפִּידִם וְאֵת קוֹל הַשֹּׁפָר וְאֶת־הָהָר עָשֵׁן וַיַּרְא הָעָם וַיָּנֻעוּ וַיַּעַמְדוּ מֵרָחֹק׃ וַיֹּאמְרוּ אֶל־מֹשֶׁה דַּבֵּר־אַתָּה עִמָּנוּ וְנִשְׁמָעָה וְאַל־יְדַבֵּר עִמָּנוּ אֱלֹהִים פֶּן־נָמוּת׃
God's response, down to the end of Deut. 5, follows a couple of verses later.
They said to Moses, Behold, the Lord our God has showed us his glory and his greatness, and we have heard his voice out of the midst of the fire: we have seen this day that God does talk with man, and he lives. Now therefore why should we die? for this great fire will consume us: if we hear the voice of the Lord our God any more, then we shall die. For who is there of all flesh, that has heard the voice of the living God speaking out of the midst of the fire, as we have, and lived? Go you near, and hear all that the Lord our God shall say: and speak you unto us all that the Lord our God shall speak unto you; and we will hear it, and do it. וַיֹּאמְרוּ אֶל מֹשֶׁה הֵן הֶרְאָנוּ ה׳ אֱלֹהֵינוּ אֶת־כְּבוֹדוֹ וְאֶת־גָּדְלוֹ וְאֶת־קוֹלוֹ שָׁמַעְנוּ מִתּוֹךְ הָאֵשׁ הַיּוֹם הַזֶּה רָאִינוּ כִּי־יְדַבֵּר אֱלֹהִים אֶת־הָאָדָם וָחָי׃ וְעַתָּה לָמָּה נָמוּת כִּי תֹאכְלֵנוּ הָאֵשׁ הַגְּדֹלָה הַזֹּאת אִם־יֹסְפִים אֲנַחְנוּ לִשְׁמֹעַ אֶת־קוֹל ה׳ אֱלֹהֵינוּ עוֹד וָמָתְנוּ׃ כִּי מִי כָל־בָּשָׂר אֲשֶׁר שָׁמַע קוֹל אֱלֹהִים חַיִּים מְדַבֵּר מִתּוֹךְ־הָאֵשׁ כָּמֹנוּ וַיֶּחִי׃ קְרַב אַתָּה וּשְׁמָע אֵת כָּל־אֲשֶׁר יֹאמַר ה׳ אֱלֹהֵינוּ וְאַתָּה תְּדַבֵּר אֵלֵינוּ אֵת כָּל־אֲשֶׁר יְדַבֵּר ה׳ אֱלֹהֵינוּ אֵלֶיךָ וְשָׁמַעְנוּ וְעָשִׂינוּ׃