I am not sure I could quite say why The Two Faces of January doesn't work, but it doesn't.
The costumes, by Steven Noble, and the score, by Alberto Iglesias, are great, and in all honesty I think this could have been a good movie. There is just something missing here. I suspect that it is the performances. Oscar Isaac, Viggo Mortensen, and Kirsten Dunst are the three central figures in the drama, but Dunst's part is underwritten, and we aren't really allowed to love any of the characters. They are all being quite cool, but none of them quite ever lets us in.
With beautiful scenery, great photography, and a terrific plot supporting them, the movie tries to hit emotional places, but none of these ever lands – our investment in the characters is just too shallow. I only cared about whether or not either of them would win; I never cared about how much it would hurt if one of them lost. So maybe it wasn't the performances; maybe it was simply the stakes of the film that were missing.
In any case and for what it's worth, Oscar Isaac continues to be someone to watch. Even though the performance is sort of off, he is quite compelling.