Contradiction with Hebrews 7:11-12
Exodus 40:15 establishes a perpetual priesthood, while Hebrews 7:11-12 discusses a change in the priesthood, implying it is not perpetual.
Hebrews 7:11-12: If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need [was there] that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
Contradiction with Colossians 2:14
Exodus 40:15 supports the continuation of priestly ordinances, while Colossians 2:14 speaks of these ordinances being blotted out or abolished.
Colossians 2:14: Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
Contradiction with Galatians 3:24-25
Exodus 40:15 implies the lasting role of the law and priesthood, whereas Galatians 3:24-25 suggests the law is a temporary guide until Christ came.
Galatians 3:24-25: Wherefore the law was our schoolmaster [to bring us] unto Christ, that we might be justified by faith.
Contradiction with Jeremiah 31:31-33
Exodus 40:15 points to a lasting covenant with the Levitical priesthood, but Jeremiah 31:31-33 predicts a new covenant that surpasses the old.
Jeremiah 31:31-33: Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Paradox #1
Exodus 40:15 talks about anointing priests to serve God forever. The potential contradiction or conflict might arise when comparing this to other parts of the Bible where the eternal nature of a priesthood is challenged, such as the introduction of Jesus as the eternal high priest in the New Testament, which might seem to replace or fulfill the Old Testament priesthood. Some may see this as inconsistent regarding the duration and continuity of the priesthood.
Paradox #2
Exodus 40:15 discusses anointing priests and giving them a perpetual priesthood. A potential contradiction could arise from the idea of inherited positions or privileges based on lineage, which might conflict with modern values of meritocracy and equality, where roles and leadership should be earned based on ability and effort, not hereditary status.