What does Moses predict in Deuteronomy?

Answer 1

• The Israelites will take the land of Canaan (Deuteronomy 31:16)
• There will be an Israelite monarchy (Deuteronomy 17)
• Some of the Israelites will stray after the Canaanite gods (Deuteronomy 31:16)
• There will be true prophets (Deuteronomy 18) and false ones (ibid ch.13)
• The Israelites will eventually be exiled, widely scattered and reviled (Deuteronomy 28)
• The Jews will regain the land of Israel (Deuteronomy 30)

Every one of these prophecies has been fulfilled.

Answer 2

Nothing. It is God who does the predicting, since Moses wrote the Torah at God's dictation (Exodus 24:12, Deuteronomy 1:3).
What does Deuteronomy predict? Some examples:

• The Israelites will take the land of Canaan (Deuteronomy 31:16)
  
• There will be an Israelite monarchy (Deuteronomy 17)
  
• The Israelites will create a place of worship (the Temple) to God (Deuteronomy ch.12 and 16)
  
• Some of the Israelites will stray after the Canaanite gods (Deuteronomy 31:16)
  
• There will be true prophets (Deuteronomy 18) and false ones (ibid ch.13)
  
• The Israelites will eventually be exiled, widely scattered and reviled (Deuteronomy 28)
  
• The Jews will return to the worship of God (Deuteronomy ch.4 and 30)
  
• The Jews will regain the land of Israel, which will prosper (Deuteronomy 30)

Every one of these prophecies has been fulfilled.

See also the Related Link:

Fulfilled prophecies