On the film's crossing of genres and the ending (SPOILERS, of course)
I recently watched this film for the first time, and loved it, for the most part. One of the things I appreciated was how it started as a straight police mystery/thriller and became a romantic drama halfway through, so that the hunt for the serial killer took a backseat to the relationship between the protagonists. As others have pointed out, the scene with Frank and Helen arguing on the street, after Frank confesses the date was police work, felt like a scene straight out of the second act of a romantic comedy.
In regards to the climactic scene, and the resolution of the mystery, Roger Ebert pointed out "the ending of Sea of Love cheats by bringing in a character from left field at the last moment. Part of the fun in a movie like this is guessing the identity of the killer, and part of the problem with Sea of Love is that the audience is not fairly treated. Technically, I suppose, the plot can be justified. But I felt cheated. I had good feelings for the characters and their relationships, but I walked out feeling the plot played fast and loose with the rules of whodunits."
Ebert is not talking without reason. I feel his complaint is thoroughly justified when one looks at the film as a mystery/thriller: the character of Terry is presented early on and has a part in shaping the film's plot, by providing a red herring, so he feels reasonably well integrated into the structure of the story, but beyond the initial stake-out idea, Frank barely has any agency in finding out he is the killer. He just happens to get involved with his ex-wife. Once again, from a mystery/thriller point of view, this is a clear weakness. We expect Frank to pursue the leads and do the work to catch the guy... yet he doesn't have to: he comes to him. (Continues...)