Qur'an and the Trinity

I keep seeing Christians (mostly Catholics) beating this dead horse where they accuse the Qur'an of depicting the Virgin Mary to be part of the Trinity. When I read these two Surah's that supposedly depicts this accusation I fail to see the connection.

Sahih International Translation:
Quote:
An-Nisa:
171: "O People of the ******ure, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs."
Quote:
Al-Maeda:
72: "They have certainly disbelieved who say, " Allah is the Messiah, the son of Mary" while the Messiah has said, "O Children of Israel, worship Allah , my Lord and your Lord." Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And there are not for the wrongdoers any helpers."

73: "They have certainly disbelieved who say, " Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment."

74: "So will they not repent to Allah and seek His forgiveness? And Allah is Forgiving and Merciful."

75: "The Messiah, son of Mary, was not but a messenger; [other] messengers have passed on before him. And his mother was a supporter of truth. They both used to eat food. Look how We make clear to them the signs; then look how they are deluded."

116: "And [beware the Day] when Allah will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides Allah ?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen".
So am I right in my assumption that the Qur'an doesn't depict the Virgin Mary as part of the Trinity and the error comes from translation or have I missed something and the Qur'an does suggest such a thing?