The SAB has a trio of questions about Peter's upcoming denial, and before I even check, I seem to recall that there was some vagueness there. "Did Jesus say before the cock crow or before the cock crow twice?" and "Did the cock crow before or after Peter's denial?" and "To whom did Peter deny knowing Jesus?" I think there are definite contradictions present in all but the second question, and that's because with the cock crowing twice, it just works out that way; that is to say in a way that I don't think the second question really adds anything to the problem of the first stated contradiction. I suppose I should put in an opinion as to which I think is right; normally if it's three to one, you'd think you'd go with the three, but it's generally understood that Mark's Gospel (the one in which the cock crows twice) was told mainly from Peter's point of view, which makes me lean towards the "twice" thing. As for the third question, again there does seem to be discrepancy, and I'd lean towards Mark's Gospel, but if anything can be said in defense of the discrepancy here, he was in the middle of a large crowd, and there may have been a lot of people talking to him in the end. Beyond that, I've got nothing on these.
"Did Jesus ask God to save him from crucifixion?" I can see how this could look like a contradiction, but there's something important in all of these passages in both columns. In every telling, Jesus says that in the end, no matter what his vulnerable human body might desire, he is there to do the will of God the Father, and that means going to the cross.
"Did Judas identify Jesus with a kiss?" Well, three of the four Gospels say so, and the fourth Gospel doesn't say that he didn't, so I'm inclined towards "Yes." (The answer to the question of whether Jesus came to bring peace was addressed here with an answer of "It's complicated.")
"Was Jesus taken to Caiaphas or Annas first?" This one takes some explanation, and it may come up elsewhere. This was a unique situation in the history of Israel in which there were two high priests, one of which had been appointed by the people and the second of which had been put into the position by the Romans. Since both were serving as high priest, Jesus was probably taken before the both of them. It may not have been simultaneous, but essentially at the same time.
"Did Jesus say, 'Destroy this temple, and in three days I will raise it up'?" At first I was confused by this question, since I couldn't see the difference between the columns on the linked page; then I realized what it was: the verses in Matthew and Mark say that "false witnesses" attested to him saying this. I think you have to look carefully at the wording, and that in the John passage, Jesus is talking about the "temple" of his physical body, while the witnesses are making it to sound like he's talking about the physical temple building. I don't blame the SAB for calling this a contradiction, as it's pretty subtle.
"How did Jesus respond to the high priest?" This is another fairly subtle one, and I say that it's subtle because the three responses given are still very similar, from "Thou hast said" to "Ye say that I am" to the very straightforward "I am". All of them are answering in the affirmative, although as the SAB points out, the first two are less straightforward, but the second includes "I am" within it. A possibility is that Jesus said something like "Thou hast said that I am" and it got misheard in various ways, or he may have been asked multiple times and different responses got recorded by different authors but I'm not sure what is the best way to resolve this. As I've said previously slight difference in wording doesn't bother me in general, but this seems a bit more important, as it's a crucial moment in Jesus' trial. Leaving that hanging, however, it's worth noting that, as in modern law, a witness is not required to incriminate himself. It's one of a handful of things that made Jesus' trial illegal under Jewish law. (The SAB notes that the high priest rent his clothes, which I seem to recall also being against Jewish Law.)