Contradiction with Ezra 1:3
Ezra 6:4 mentions expenses paid from the king's treasury, whereas Ezra 1:3 seems to indicate that the rebuilding efforts were supported by the voluntary offerings of the people.
Ezra 1:3: Who [is there] among you of all his people? his God be with him, and let him go up to Jerusalem, which [is] in Judah, and build the house of the LORD God of Israel, (he [is] the God,) which [is] in Jerusalem.
Contradiction with 1 Kings 6:7
Ezra 6:4 mentions the use of great stones and timber for construction, whereas 1 Kings 6:7 states that no sound of hammer, chisel, or any iron tool was heard during the Temple's construction, implying a quieter process.
1 Kings 6:7: And the house, when it was in building, was built of stone made ready before it was brought thither: so that there was neither hammer nor axe [nor] any tool of iron heard in the house, while it was in building.
Contradiction with Acts 7:48
Ezra 6:4 addresses building a physical house for God using costly materials, whereas Acts 7:48 states that the Most High does not dwell in houses made by human hands.
Acts 7:48: Howbeit the most High dwelleth not in temples made with hands; as saith the prophet,
Contradiction with Hebrews 9:11
Ezra 6:4 emphasizes the importance of physical structures for worship, while Hebrews 9:11 speaks of a greater and more perfect tabernacle not made with hands.
Hebrews 9:11: But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
Contradiction with John 4:21
Ezra 6:4 focuses on constructing a specific worship place, whereas John 4:21 relates to worshiping God not confined to a particular 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.