Contradiction with Matthew 6:5
Acts 20:20 describes teaching "publickly," whereas Matthew 6:5 suggests avoiding public demonstrations of piety.
Matthew 6:5: And when thou prayest, thou shalt not be as the hypocrites [are]: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward.
Contradiction with Matthew 5:14-16
Acts 20:20 speaks of open teaching, while Matthew 5:14-16 might suggest being discreet in acts for personal glory.
Matthew 5:14-16: Ye are the light of the world. A city that is set on an hill cannot be hid.
Contradiction with John 7:10
In Acts 20:20, Paul seems open about his activities, but in John 7:10, Jesus moves in secret.
John 7:10: But when his brethren were gone up, then went he also up unto the feast, not openly, but as it were in secret.
Contradiction with Acts 17:17
Paul debates publicly in Acts 17:17, which appears consistent with Acts 20:20 but could be seen as contradictory about the manner of teaching.
Acts 17:17: Therefore disputed he in the synagogue with the Jews, and with the devout persons, and in the market daily with them that met with him.
Contradiction with 1 Corinthians 14:28
Acts 20:20 involves public dissemination of teaching, while 1 Corinthians 14:28 advises silence when there's no interpreter for unknown tongues, promoting private edification.
1 Corinthians 14:28: But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God.
Contradiction with Matthew 10:27
Acts 20:20 focuses on public teachings, whereas Matthew 10:27 encourages proclaiming in light what is heard in the dark.
Matthew 10:27: What I tell you in darkness, [that] speak ye in light: and what ye hear in the ear, [that] preach ye upon the housetops.