Contradiction with Numbers 20:14-21
Numbers 21:1 mentions the king of Arad fighting Israel, whereas Numbers 20:14-21 describes Israel requesting passage through Edom without mention of aggression from Arad.
Numbers 20:14-21: And Moses sent messengers from Kadesh unto the king of Edom, Thus saith thy brother Israel, Thou knowest all the travail that hath befallen us: [befallen...: Heb. found us]
Contradiction with Numbers 33:40
Numbers 21:1 states the King of Arad heard of Israel coming by the way of spies, while Numbers 33:40 states he heard Israel was coming by the way of Atharim.
Numbers 33:40: And king Arad the Canaanite, which dwelt in the south in the land of Canaan, heard of the coming of the children of Israel.