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. (02:17:40)
Revealing mistake: Near the end of the film, when people are running in terror out of the theater and into Times Square, you can see that the people are not leaving any footprints in the snow. The snow must have been digitally added to the scene.
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.
Revealing mistake: Despite being thrown, falling, being dragged and various other things, Ann's hair and face are almost always clean. Even when there does appear to be some dirt, in the next shot they are clean again.
Revealing mistake: The crew is sailing to the island and the rough sea makes the boat move violently. Jack Driscoll stumbles but the things in his cabin don't move at all, or at least don't cause the chaos they should. Obviously the only thing moving is Jack and the camera.
Revealing mistake: When the longnecks are tumbling down the hill it's obvious there's a screen behind Preston and Jimmy and Hayes.
Revealing mistake: When Ann is in Kong's hand for the first time you can see a screen bounce behind Ann.
Revealing mistake: As Kong and Anne Darrow exhale in the freezing New York air there are many shots where you can't see their breath frosting up as it comes out of their mouths.
Revealing mistake: When Kong is shaking the tree down it's obvious that there's a screen behind the film crew when they fall.
Revealing mistake: When they are all running from the dinosaurs you can see where they should have been crushed by the massive brachiosauruses. Also when they are running along the collapsing mountainside they are somehow able to float along as the ground is giving way.
Revealing mistake: In the chasm scene, when Lumpy is fighting off worm-like creatures, we can see that his sword is made of rubber.
Answer: I assume you mean, could the building take his weight, not whether an ape would really have the ability to climb a building (if that's what you mean, then it's definitely yes...apes are great climbers). Assuming Kong is proportionally as heavy as normal-sized gorillas, which tend to be in the area of 160kg (~350lbs), then he weighs over 80,000kg (89 tons, give or take). The average human weighs about 62kg, so that's about 1,300 humans, and the capacity of the ESB is over 13,000. So, assuming the building is mostly, or even half, empty while a giant gorilla scales it, the building could handle his weight.
Keep in mind, though, that the weight allowance for the building assumes people on the floors of the building, not climbing on the outside. The outer structure of a building isn't designed for massive creatures climbing on it. While the building as a whole would likely survive, there would be significant damage as Kong would be breaking windows and pulling stone off it as he made his way up.