I think the problem with the star can be viewed from a few different angles, but this is what my understanding of the problem is:
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According to the Gospel of Matthew, the star over Bethlehem is not just to make the Nativity look pretty: it is a sign of Jesus’ divine favor and kingship that allows the Wise Men/ Magi to find him. By giving the star a “just so story” explanation, some Christians feel that it cheapens the miracle of Jesus’s birth, and takes God out of the Christmas story. (Even if Doctor Who is a work of fiction.)
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Personally, I saw the final gag about the Villengard star being the Nativity star coming from a mile away. To me, the combination of star+ Christmas+ anytime in history only had one solution (First century Judea). It pained me to have to wait there for the last seven minutes or so so that Moffat could show off how clever he was by placing the star in the most obvious place he could put it.
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Despite not really enjoying the ending, I liked the Time Hotel setting, and was thrilled to see the classic Moffat standards of the bootstrap paradox and long way round return. I’d probably put this one in the middle of the Christmas special heap.