When we think of the rising action of a plot we need to recall that it consists of a series of events that serve to increase the suspense and tension before the highest point, the climax. Certainly in the novel we are presented with a number of incidents that serve to raise curiosity about Kurtz but also show us the brutality of colonialism. Think of the "grove of death" with the accountant in his starched white suit just next door, and then the station where they are delayed because they are waiting for ratchets. Then the actual last stage of the voyage to the "heart of darkness" with the Russian and then the grisly description of how Kurtz has "decorated" the place.
In the film, the rising action is different. I remember very vividly the increasing sense of claustrophobia and madness, occasionally breaking out as these incredibly young soldiers are stretched to breaking point. They stop a Vietnamese boat against Marlow's instructions, and end up killing the family on board because the girl doesn't want to show them a puppy that is in a box she is sitting on. They stop in a hot spot where the commanding officer makes his soldiers surf in the sea whilst a bombardment is going on. One of the soldiers on the boat plays with purple flares to the sounds of "Purple Haze" by Jimmy Hendrix. To me, the rising action of the film is to emphasise the complete surreal experience that Vietnam was, whilst in the book it serves to increase our suspense before we finally meet Kurtz and also to show the reality of the colonial endeavour.