After her return from Rome Beth receives a phone call from Joan, informing her that she is "front page news" due to her climbing into the Fountain of Love. A cutaway shows a newspaper with the headline "Stupidissima". This translates not simply as "stupid", but rather as "the pinnacle of stupidity".
The scenes in the Guggenheim Museum were filmed during an actual exhibition by Cai Guo-Qiang called "I Want To Believe": The cars in the main entrance suspended from the roof was a piece entitled "Inopportune: Stage One"; The tigers with arrows protruding from them is "Inopportune: Stage Two"; The taxidermy wolves (which the coin rolls between as Beth runs after it) is a piece entitled "Head On".
People throwing coins into the Fontana di Trevi, the reputed Fountain of Love in Rome to have their wishes granted in matters of the heart is true; in fact, it's an offense to try to steal coins from the fountain because it's the same as stealing other people's wishes.