Although Roosevelt Island in the Potomac across from Georgetown was so designated in the 1930s, locals referred to it by its former name of Mason's Island until the Theodore Roosevelt memorial was erected on it in 1966, two years after events in the movie. Access in the mid-1960s was by a very small ferry from Georgetown, making it a somewhat unlikely location for a discrete rendezvous of an illegal nature.
Alex spills ice cubes on the sofa, but they have disappeared by the time he has finished recalling Louie's and Corinne's wedding (there's not enough time for them to have melted, although he could have been clearing up while we weren't looking).
During the seduction between Alex and Corinne in front of the sofa, as they are disrobing you can see that Corinne is barefooted. As Philip enters the room and the fight scene begins there is a quick shot of Corinne with shoes now back on her feet.