We're going to be honest: we're not so sure about this guy for most of the film. Sure, Dumbledore embraces Karkaroff, the headmaster at Durmstrang, when he arrives with his students for the Triwizard Tournament…but still, there are some things that make us nervous about him.
First: we see him sneak into the room that houses the Goblet of Fire and close the door. What is that about? Why would he be doing that? Is that how Harry's name makes it in there? (Spoiler alert: it's not, but we don't know that right away.)
And then there's the fact that Karkaroff used to be a Death Eater. Yeah—he was one of Voldemort's cronies. He was actually imprisoned in Azkaban and squealed on fellow Death Eaters to get leniency. At a hearing that he requested, he went through a laundry list of names that were of no interest to the wizarding powers-that-be until he dropped a huge bombshell:
KARKAROFF: I know for a fact this person took part in the capture and, by means of the Cruciatus Curse, torture of the Auror Frank Longbottom and his wife!
BARTY CROUCH SR.: The name. Give me the wretched name!
IGOR: Barty Crouch…Junior.
This is big news because Barty Crouch Senior is a big mucky muck in the Ministry of Magic's law enforcement group. And oh yeah, he's actually presiding over the hearing in question.
So, we suppose that is why Igor is now free and actually allowed to teach wizarding—that was some pretty important intel.
Regardless of how much Igor has reformed, he still bears the Dark Mark on his arm with which Voldemort branded all his followers, and it starts to burn as Voldemort gets closer and closer to coming back. Harry catches him freaking out about the mark to Snape.
Which makes sense: even if Karkaroff is still secretly hearting Voldemort (the film kind of leaves that open), he betrayed the Dark Lord and his fellow Death Eaters to get freedom. So, he's gotta be even more nervous than the average wizard.