The business with the old lady and her lost-then-found dog does have a reason for being in the movie. It's always a hefty clue when a filmmaker places something at the beginning or end that it IS something especially significant. In this case it has to do with the entire meat of the story (not to be confused with its distractions) and is emphasized by its placement at BOTH the beginning AND the end of the movie. The tiny, seemingly random tale of the old woman and her dog thereby brackets everyone else's story. Why?
The central question of the movie is, is simple comfortable domesticity with another being enough? Enough to give up your ideals, however out of whack they may be, enough to really confront your personal issues, enough to turn down the chance to explore intriguing new territories with someone else? Is it worth everything you go through and give up just to save a relationship that seems closer to mere companionship than to your earth-shattering romantic fantasies? One look at the old lady's face when she stares at her dog's empty dish, and then again when she sees him limping back to her, will give you the filmmaker's answer.
The central question of the movie is, is simple comfortable domesticity with another being enough? Enough to give up your ideals, however out of whack they may be, enough to really confront your personal issues, enough to turn down the chance to explore intriguing new territories with someone else? Is it worth everything you go through and give up just to save a relationship that seems closer to mere companionship than to your earth-shattering romantic fantasies? One look at the old lady's face when she stares at her dog's empty dish, and then again when she sees him limping back to her, will give you the filmmaker's answer.