At the Natural History Museum, Barney says that the last time he saw his Uncle Jerry was in July 23rd 1981 when he was 6 after he knocked down the Blue Whale Exhibit. In "Hopeless", They say that it is September 1983 when they last saw each other. In a related subject Barney would not have been 6 in 1981. In episode #1.15 "Game Night", Barney tells his story about Shannon and states that it happened in 1998 and that he was 21. This means he was born in 1977. He would have been 4 in 1981.
When Barney and Robin were touching the statue, you can see Robin in the background drink her wine too early, spit it back in her cup, then wait to drink it when Barney does.