In Goblet of Fire (The Parting of the Ways), Dumbledore says to Snape:
“Then go down into the grounds, find Cornelius Fudge, and bring him up to this office. He will undoubtedly want to question Crouch himself. Tell him I will be in the hospital wing in half an hours time.”
Later, in the hospital wing:
“You should never have brought it inside the castle!” yelled Professor McGonagall. “When Dumbledore finds out–” […]
Snape:
“He insisted on summoning a Dementor to accompany him into the castle. He brought it up to the office where Barty Crouch –”
And McGonagall:
“I told him that you would not agree, Dumbledore! I told him you would never allow Dementors to set foot inside the castle, but –” […] “The moment that – that thing entered the room,” she screamed, pointing at Fudge, trembling all over, “it swooped down on Crouch and – and –”
Snape and McGonagall both saw the Dementor before he came into the room, knew that Dumbledore would disapprove and knew what a Dementor could do. Both knew how to do a Patronus charm and it seems to me that at least McGonagall saw the Dementor executing the kiss. McGonagall had orders to protect Barty Crouch, she and Snape had time to talk to Fudge about the Dementor but nobody did something about it. For starters, they could have insisted on talking to Dumbledore before letting a Dementor in the school (especially since Dumbledore didn't even let Dementors in the castle when everybody thought Sirius Black was running amok in there in the third year).
So why didn't they do anything to stop it?