Contradiction with Exodus 28:41
Whereas Exodus 40:13 focuses only on Aaron, Exodus 28:41 includes both Aaron and his sons in the anointing process, suggesting a group ordination rather than an individual one.
Exodus 28:41: And thou shalt put them upon Aaron thy brother, and his sons with him; and shalt anoint them, and consecrate them, and sanctify them, that they may minister unto me in the priest's office. [consecrate...: Heb. fill their hand]
Contradiction with Numbers 3:3
Exodus 40:13 speaks specifically to Aaron, but Numbers 3:3 expands the consecration to his sons as priests, contradicting the singular focus on Aaron in Exodus 40:13.
Numbers 3:3: These [are] the names of the sons of Aaron, the priests which were anointed, whom he consecrated to minister in the priest's office. [whom...: Heb. whose hand he filled]
Contradiction with Hebrews 7:27
Exodus 40:13 establishes the priesthood through Aaron's consecration, but Hebrews 7:27 speaks of Jesus as the high priest who does not need daily sacrifices, arguably rendering Aaron's priesthood unnecessary according to New Testament theology.
Hebrews 7:27: Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself.