The past scenes in Blue Valentine were all shot on film to achieve a more nostalgic feel, like looking back on fond memories. This also meant fewer takes as they only had a certain amount of film to shoot with, and only used one camera. This results in the couple always being in the frame together for majority of the shots.
These moments are almost always accompanied by the soundtrack too.
A lot of the scenes were unscripted and improvised by the actors, as the director Derek Cianfrance used various method techniques to create these moments, which is why all the scenes are hand held, adding to the spontaneous feeling of the past section of the film.
The future/present scenes were shot with digital cameras, mostly on tripods and long lenses, creating a more distant feeling. These scenes are shot in a traditional shot, reverse shot way, meaning we don’t see the couple in the same frames anymore.
The soundtrack never accompanies these moments until the end, making the future/present section of the film feel more empty.
In between filming the past and present parts of the film, Ryan Gosling and Michelle Williams stayed in a house together for a month, encouraged by the director to pick fights and argue with each other, so when it came to filming these scenes, the arguments would feel real, tiring and repetitive. Shooting on digital also meant they had more time for more takes, which would really emphasize the worn out feeling of the dialogue exchanged, opposed to the fresher, unrehearsed performances of the past.