I've just noticed this site containing a discussion of Confrontation. (Note: Kol Dodi Dofek is available online, as well as some of his articles on traditiononline.org.) including one article by my favourite author Prof. Marc Shapiro. I am somewhat surprised that no mention was made of the locus classicus for the subject - R' Hai Gaon's query of the local Christian priest cited here along with some other sources - based interestingly enough on R' Dovid Tzvi Hoffmann's Der Shulkahan Arukh. See also this article for a Christian view (note especially the conclusion) from the Boston of 1858.
R' Yaakov Emden's comments in his hagahot to Seder Olam are well known. These comments caused him some difficulties from less enlightened members of the community, as he describes in Part 2 of his Sefer Shimush - and see also his hagahot to Shevet Yehuda on the Christian- Jewish dialogues contained therein - published in Tzefunot by T. Leherer. See also the introduction to Kreisi U' Pleisi for the position of R' Yonosoan Eibschutz.
Sinec we are nearing Rosh HaShana it is worth citing Y. Leibes's article on the strange reference to a Yeshua Sar Hapnim in the Yehi Ratzon preceding the Tekios (removed I think in the Artscroll machzor - must check). I have already posted about strange mentions in some of the kabbalistic tefillos in the past.