Writers' theologies and creative liberties
The trial: Pilate did not wash his hands of Jesus blood because they wanted a black and white bad guy
The resurrection: the events of the resurrection made the disciples all appear to be scared even after visiting the tomb, also the two disciples interaction with Jesus on the road to Emmaus is not shown, which is essentially when they realize all scripture was being fulfilled
Jesus' time with the disciples: the time between his resurrection and ascension was 40 days, but the events in the show made it look like a few days, and this time was not spent reminiscing about the good ol' days as the show depicts- Jesus was teaching them about the Kingdom of God. The first time Jesus appeared before the disciples, he breathed the Holy Spirit into them, the show neglects this. Thomas also didn't see Jesus until eight days after he says "Unless I see in his hands the mark of the nails, and place my finger into the mark of the nails, and place my hand into his side, I will never believe.", he also says "My Lord and my God" when he does see him, which the writers chose to leave out.
Pentecost and the choosing of another apostle: There were at least 120 people in the running to be a new apostle, the show doesn't show that more than 11 and the 4 women were aware of Jesus' resurrection, but the 120 mean that they were probably part of the 500 who saw the resurrected Jesus from 1 Corinthians 15:6, they chose a new apostle, Matthias. The show depicts them reciting The Lord's Prayer like a chant to entice the Holy Spirit to come, which is a ridiculous portrayal. The 120 were present when the Holy Spirit came and 3,000 were converted.
On a side note, when Peter speaks about the Holy Spirit to his daughter, they both say "it" but the Holy Spirit is a person.
So what does it say about the writers' theologies? They don't want to say Jesus is God and they don't want to say the Holy Spirit is a person. They've shown their beliefs to be more Jehovah's witness than Reformed. They deny Jesus' divinity and neglect the Holy Spirit's role as part of the Trinity.
They are also more concerned with having a "Game of Thrones" comparison by showing a tense political battle than staying true to the source material.