With Islam the Holy Spirit becomes a mere angel, and God himself has no spirit as such.
Wrong. In Islam, the Spirit and angels are two different types of beings.
The Day that the Spirit and the angels will stand in rows, they will not speak except for one whom the Most Merciful permits, and he will say what is correct. (78:38)
Because there are both good and evil angels, Isalm has problems identifying which angels are good and which are evil. How can one even know whether Mahomet was possessed by a good angelic spirit, or a bad one?
The idea that there are good and bad angels is a distinctly Christian one. In Islam all angels are good, so there's no question of identifying good angels from "bad" ones.
Christianity has that problem. Remember, the New Testament says "Satan disguises himself as an angel of light" (2Corinthians 11:4).
So there is a serious issue with the credibility of the witnesses in Islam.
It's Christianity and the Bible that has that serious problem. For example, the 4 accounts of the Gospels give us 4 varying accounts of the one most important event in Jesus' earthly life, his crucifixion.