While filming, Ben Stiller and Owen Wilson only had one day that they saw each other. Stiller talked to a toothpick for the Jedediah scenes, then three months later Wilson came in and filmed all of his parts.
The TV news report mentioning cave drawings in the subway shows a quick shot of the 81st St. subway station in New York, which is indeed the correct subway stop for the American Museum of Natural History. Many NY subway stations include wall tiling that incorporates mosaics and artistic patterns in themes related to the station's neighborhood. The subway cave drawings shown in the film are actually part of the tile art in the station, relating to the museum itself.
The building featured in the film, which was constructed on a sound stage in Vancouver, Canada, is based on the American Museum of Natural History in New York City, external shots of which were used in the movie.
On the wall of the elevator and in the lobby, signs on the wall can be seen with titles paralleling what is happening to Larry at that point in the movie, including: "Spineless" and "Weathering the Storm".