When Ted shows the page of the newspaper about the Arcadia, the topic at the left side is about the place where Marshall and Lily live, "DOWISATRIPLA". And on the right side is a scoop about the "Cockamouse" from the 1st season. There is even a quote saying "No one is safe, not even your Mother.
Lily says, "We'll make it work." to Marshall referencing the pilot when Marshall admits he loves olives.
When Ted is using the architecture of the building to whisper across the museum, this is actually possible. While it cannot confirm that this is possible in the New York museum that they were in, This is possible in The Union Terminal building in Cincinnati, Ohio which coincidentally is Cincinnati's History Museum. There are two water fountains on opposite sides of the dome in the entry way where you can speak across the crowded room as if you were right next to each other.
Arthur introduces the Captain as George Van Smoot. This is the same surname as Michael York's character in Robots vs. Wrestlers (2010) and also same name as the Van Smoot House title/tt0760776/?ref_=ext_shr_lnk.
During the "anti-establishment" flashback, as Marshall and Lily mock Russell in his "monkey suit", Marshall is eating a very large "sandwich", which in How I Met Everyone Else (2007) was established as a euphemism for smoking a joint.