Harry is helped in the 3 tasks by being told what is involved, or by given clues. A friend gives Harry a special plant to swallow so that Harry can stay underwater for an hour in the 2nd task. Harry does not find out things on his own but is given help by others. This cheating is presented more strongly in the book. It turns out that the false Prof. Moody engineered this so that Harry would be in the Tournament to be endangered and later captured.
Some would say that Harry redeems himself by his acts of bravery during the Tournament in saving people in the 2nd task, and in rescuing another contender during the 3rd task (though this contender, Cedric, gets killed a short while later). While it is true that Harry is brave and unselfish in doing these rescues, it does not negate the cheating (or the emphasis on magic), though the cheating in the book is more pervasive (as is Harry's lying).
One scene involves Harry in a large spa-like bath where he sits naked while trying to figure out the clue for the second task. Moaning Myrtle, a ghost (she was a student who was murdered several years ago), flits about Harry and gives him hints about the clue, all the while trying to get a peek at his private area.
Harry is helped by the ghosts of his dead parents, and by the magic in his wand, during the final showdown with Voldemort.
After a frightening run through a large maze in search of the Goblet of Fire, Cedric and Harry end up in a cemetery where Cedric is killed by Voldemort. The portrayal of Cedric's death is vivid and wrenching. There is nothing subtle about it. Later, after Harry brings Cedric's body back to the school grounds (after his death, Cedrick's "ghost" asks Harry to take his body back), the audience sees Cedric and the open-eyed expression of death on his face. Showing this is entirely unnecessary, especially for a PG-13 movie that the filmmakers must know a lot of children under 13 will attend.
Harry is tied up, and a ritual is performed by Voldemort's aide, Wormtail. In a cauldron, Wormtail places a bone from Voldemort's dead father, cuts off his own hand for the "brew," and cuts Harry's arm deeply, adding Harry's blood to the mix. The disembodied substance of Voldemort is placed in the cauldron and he comes out of it in a bodily, though hideous, form..
Due to this ritual, which is intensely horrifying in the movie, Voldemort now has Harry's blood in his body. This serves to further strengthen the connection between Harry and Voldemort. They share the feather of the same bird in their respective wands; they both speak parseltongue, the language of snakes; Harry's scar, inflicted when Voldemort tried to kill him as an infant, hurts and burns when Voldemort is near or is after Harry; Harry is able at times to have a psychic vision of what Voldemort is doing; and now Harry's blood runs in Voldemort's veins.
What is the purpose of this connection? As with the connection between Luke Skywalker and Darth Vader in the Star Wars movies, the connection shows the light and dark side of magic (the Force in Star Wars). This is not about good and evil so much as it is about using power. The source for both the dark powers of Voldemort and for the sorcery of Harry and Dumbledore is the same. The indication in the books is that those who become dark wizards do so from their own will; that is, it is entirely under one's control as to whether one is a dark or white magician. The message is that as long as one chooses to use these powers for good, then one is good.