Audio problem: After the scene where the men had to fight off the giant bugs, there is a wide shot where the men can be seen being helped out of the pit by the captain and a few extra crewmembers. The captain is shouting something, however, if you look closely, his mouth is not in sync with what he is saying.
Audio problem: When Carl tells Preston to show Ann on board the ship he says something like, "Hello, Miss Darrow, I'm Mr. Denham's assistant." His lips aren't properly synchronized with the dialogue when he says this.
Audio problem: When the ladder Ann was standing on hits the ridgy part of the Empire State Building there is no loud crash.
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.