Contradiction with Numbers 12:6
This verse states that God speaks to His prophets in visions and dreams, whereas Luke 1:11 describes an angel appearing directly to Zechariah.
Numbers 12:6: And he said, Hear now my words: If there be a prophet among you, [I] the LORD will make myself known unto him in a vision, [and] will speak unto him in a dream.
Contradiction with John 1:18
This verse says no one has seen God at any time, yet Luke 1:11 describes an angelic presence suggesting divine interaction.
John 1:18: No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared [him].
Contradiction with Hebrews 1:1
This verse mentions that God used to communicate through prophets, while Luke 1:11 depicts an angel communicating directly, not through a prophet.
Hebrews 1:1: God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,