Why did Igor Karkaroff enter the Great Hall?

Only theory I've ever considered was that he "fixed" the goblet to ensure that Krum's name was pulled from the flames. Other than that, he really had no business being in that room. Whether he actually has the skill to manipulate such a magically powerful object... possibly. He was a headmaster, after all. That has to say something about him.

Recalling the conversation between fake Moody and Igor, Moody does say that only a very powerful Confundus charm could hoodwink the goblet, so perhaps there is some way to do it, if you're powerful enough.

No, no, no - That WASN'T Karakroff! It was Barty Crouch Jr., going in to put Harry's name into the goblet; he was using his Polyjuice to disguise himself as Karkaroff in case someone else came into the room and caught him tampering with the Goblet.

Sure it made him look suspicious but I think was happened was that he cast some sort of spell on it so that Victor Krum would get picked for the Durmstrang triwizard champion.

In future scenes he is shown to be very passionate about winning so it makes sense that he would do something to cheat in order to get his best abled pupil and Quidditch World Cup player to represent the school in the tournament.

But that is just what I think.

I suppose that he might've been trying to hoodwink the goblet of fire into choosing Viktor Krum, one of his students that was also a famous Quidditch player.

I have always said it was Igor Karkaroff who put Harry’s name in the Goblet of Fire. Two people have said he was in the hall to make sure Krum’s name was chosen, and another person said it was Barty Crouch Jr. disguised as Karkaroff through Polyjuice potion.

But during the scene when Harry’s name comes out of the Goblet of Fire, you can see by the look of Karkaroff’s face his face that he was expecting Harry’s name to come out.

And again during the first task when Harry is being battered by the dragon, Karkaroff is laughing menacingly.

I think for a lack of better words, this was an in-movie red herring. There are not one but two scenes where we get the red herring. The entering of the great hall, and when the Goblet of Fire chooses Harry, we get a close-up on Igor's face. It's entirely possible that it was Barty Crouch Jr. disguised as Igor to Harry's name in. Ever since I saw GoF, I always suspected Igor himself wanted to enter into the contest for fame and glory but that was just my theory. Overall, probably just a red-herring to make Igor seem like the bad guy so the audience could not or would not suspect the half-mad Mad-Eye Moody.