Although the film provides an obvious interpretation, there are many ways to construe the eponymous visitor: as one of several guests, not all of them invited, in a New York apartment; as a visitor to the US; even as a visitor to one's own life when one becomes unmoored in the aftermath of a trauma. The story concerns a recently widowed academic, still at sea (and perhaps not only because of his grief), and his encounter with a young couple, both illegal immigrants.
While other films have tackled the world of illegal migrants with great skill - Stephen Frears's Dirty Pretty Things is a fine recent example of the power dynamics that exist in so many immigant stories - Thomas McCarthy's film unfortunately feels extremely obvious (an example: the lead character's specialty is the economics of the developing world). As soon as the central characters meet, it's not hard to foresee the manner in which the grieving Walter (Richard Jenkins) is brought out of his shell by a happy-go-lucky, Syrian drummer (and his less relaxed Senegalese girlfriend): somewhere, Edward Said is rolling in his grave.
While that's by no means the only thread to the story, it's hard not to feel that the further developments, mostly regarding the immigration system, reinforce the liberal sense of the current US political direction without acknowledging that many of the systemic problems may have (substantially and even severely)worsened since 2001 but were hardly unknown prior to that date. At the show I attended, a woman yelled out, "Don't forget to vote next fall", as if a change of party would solve the problems depicted onscreen; if only it were that simple.
In the film's defence, while there are fundamental problems with the story there are moments of tremendous warmth and humour, skilfully played by Jenkins and the much less familiar supporting faces (Hiam Abbass is especially good, capturing a character caught between aspirations for her family and blunt reality), which, scene by scene, feel strikingly real and unforced.