Contradiction with John 3:22
This verse describes Jesus and his disciples baptizing with water, whereas Acts 1:5 mentions that the disciples will be baptized with the Holy Ghost, not with water.
John 3:22: After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized.
Contradiction with Matthew 3:11
John the Baptist speaks of baptizing with water for repentance but mentions that Jesus will baptize with the Holy Ghost and with fire, which could imply a difference in timing and emphasis from Acts 1:5.
Matthew 3:11: I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and [with] fire:
Contradiction with Mark 1:8
Similar to Matthew 3:11, this verse contrasts water baptism with being baptized with the Holy Ghost, suggesting a different method and fulfillment than Acts 1:5 implies.
Mark 1:8: I indeed have baptized you with water: but he shall baptize you with the Holy Ghost.