Contradiction with Exodus 20:4
Leviticus 16:12 involves creating a specific ritual for worship, whereas Exodus 20:4 prohibits making any graven image or form for worship.
Exodus 20:4: Thou shalt not make unto thee any graven image, or any likeness [of any thing] that [is] in heaven above, or that [is] in the earth beneath, or that [is] in the water under the earth:
Contradiction with Matthew 15:11
Leviticus 16:12 details ritualistic cleanliness, while Matthew 15:11 suggests that what goes into the mouth does not defile a person, but what comes out of the mouth does.
Matthew 15:11: Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.
Contradiction with Hebrews 9:9-10
Leviticus 16:12 focuses on physical rituals for purification, whereas Hebrews 9:9-10 indicates that these rituals cannot truly perfect the conscience of the worshiper.
Hebrews 9:9-10: Which [was] a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience;
Contradiction with Colossians 2:16-17
Leviticus 16:12 prescribes specific feasts and rituals, while Colossians 2:16-17 argues against being judged on matters of ritual observance.
Colossians 2:16-17: Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath [days]: [in meat...: or, for eating and drinking] [respect: or, part]
Contradiction with John 4:21
In Leviticus 16:12, worship involves specific place-based rituals, while John 4:21 suggests that worship will not be tied to a specific location.
John 4:21: Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father.