With regard to trinity, I have a very logical debunk which to date I have not seen anyone else notice:
If Trinity polytheism is warranted theology stemming from the Old Testamen mental gymnastics the Trinitarians claim, then before Jesus's pbuh birth on earth, there must have beena duality of theology - in the vein of "God and Holy Spirit" being worshipped together... yet in the Old Testament, the Holy Spirit is not an object of worship, so how did the Christians get from 1 God to 3 and miss out the 2???
You follow?
I'll tell you how.
Constantine the Roman polytheist who was of the trinitarian cult of "Mithraism" canonised the bible (read as butchered it) in order to interpolate a tinitarian theology. You may ask why he did such a thing? It was to consolidate an already dwindling empire but factoring in the Christians as part of the Roman empire, so as to increase their numbers and therefore, taxes. it was sheer pragmatism on his behalf. Circa 325CE.
Paul (who was alive around and after the time of Jesus pbuh and was a Roman citien) was rejected not only by the apostles of Jesus pbuh but also the Jews, (paul was hitman, a mercenary hired to kill the early Christians and then became a Christian himself and claimed to be an apostle of Jesus pbuh when he never even met Jesus pbuh once in his life).
The Jews of Jerusalem tried to kill Paul for his blasphemies (oh did he blaspheme) and the Jews and the Christians were united in their hatred of him, guess who came to his rescue? The Romans - they shielded him and told him to "preach to the gentiles", another corruption seeing as Jesus pbuh was only "sent to the lost sheep of Israel.
Hope this clarifies for you why the "red letters" are important.
Scimi
Ok, three things. One- I have heard exactly this argument before, although it's not all that common outside of Islam. An incredibly similar argument was made to me by a Christadelphian. That would be a non-Trinitarian restorationist group that began in England and was initially made up of ex-Anglicans. This particular Christadelphian church just happens to be situated right next door to an as-yet-partially-built (but somewhat functional and in-use) mosque. Not your kind of mosque though, it's an Ahmadi mosque. It's quite an interesting situation.
Second. There are certain phrases in the Old Testament that hint and suggest at some sort of plurality when it comes to God (let us make man in our own image is one), and up to a certain point there were some reasonably well-developed schools of thought within Judaism (not just a comment or two here and there) considering some different possibilities of how that could be interpreted. As soon as Christianity came along though, that ceased to be a place of lively debate and things were clamped down pretty quickly. Something more orthodox was settled on, and that discussion was no more. But at one time, there was something happening there.
Third, Constantine was not a theologian, nor was he very much of a Trinitarian (although his points of view shifted a bit over time). Constantine, on the whole, was more sympathetic to Arianism than he was to the Trinitarian formula, and the First Council of Nicea affirmed the Trinity in spite of his preferences rather than because of them. Here are some quick facts. Constantine was converted to Christianity by an Arian. Constantine had some family that was Arian, one of which was an Arian priest. Not that Arians had formally broken away from the Catholic Church, of course, he would have called himself a Catholic. But he did believe in Arian doctrine. And that slightly distant family member, the priest who was Arian, is the priest that baptized Constantine just hours before his death (because Constantine wanted to save it to the end, which is something that the Catholic Church would now consider a problematic way of handling the sacraments). Also, after initially exiling Arius at the behest of the Council that reached a conclusion he didn't really like, Arius wrote a letter to Constantine and tried to change his mind about the exile. It worked, and Constantine recalled Arius and exiled Athanasius instead (he's the main defender of the Trinity). It wasn't until he died that other rulers arranged for Athanasius to return and for Arius to be exiled again, but then Constantine's son, Constantinius, followed the example of his father (his son leaning toward Arianism as well) and he recalled Arius from exile for the second time and exiled Athanasius for a second time. (After Constantine the empire was initially split into three parts under the rule of three different sons, one who supported the Trinity, one who supported Arius, and one who was pretty much indifferent, but then it later came entirely under the control of the Arian supporter....which is one main factor that necessitated Nicea II....)
Anyway, the point is that the emperors of this time period, even speaking more broadly than this, did not determine the outcomes of these councils. They had their preferences, these preferences are known to us, but they actually didn't get what they wanted. At least not when it came to the Trinity. The Arian controversy (which hinged on the question of Jesus' eternal existence more than anything else) was principally decided by bishops from Egypt, Turkey, and Syria, if we're going to use modern-day countries. And it took almost a century of arguing and controversy before everything was pretty well settled- and that was due in part to the fact that Constantine, Constantinius, and quite a few others (not necessarily all emperors) either did not support the Trinity or felt that it shouldn't be trying to suppress other ideas or they just liked the Arian ideas better. In the specific example of Constantine, he didn't know very much about it at first (and never became anything close to an expert) but he did like the Arian perspective better, and he did plenty to act that way as well.
So basically, this idea that Constantine made the Trinity happen is a common idea that you'll hear a lot from non-Trinitarians, but it's a lot more complicated than that and it's basically inaccurate when you really get down to it.
Here's a link that shows you a timeline of the Arian controversy.
http://ecole.evansville.edu/arians/arianchr.htm