Revealing mistake: When Carl is standing next to Kong's unconscious body saying, "His name will be in lights on Broadway," look at the Venture in the background. Even though it's not stuck on anything, and despite the choppy waves, it doesn't move ANY. Even if anchored, it would still bob gently in the waves; instead it's frozen solid. Obviously green-screened, or possibly a matte painting.
Revealing mistake: When Ann is juggling for Kong on the cliff edge she starts juggling at one point. If you look closely, you can see that she is simply moving her hands, and the rocks have been added digitally. This is most obvious when she leans right back, and the rocks don't match her hand movements at all.