Continuity mistake: When Anne is on the rotten tree branch, trying to escape the giant lizard, there is a large black leaf on her chest, but, in the next shot, it's gone.
Continuity mistake: At the end, planes are attacking Kong on top of the building. They stop when they see Ann up there. At one point she is standing, hugging Kong's arm. The camera angle changes to a wide shot and shows her about ten feet away and standing up from a crouched position.
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.