Maybe this is a cheap shot (Ba-da-DAH) at a thoughtful insight, but Betty shooting at the pigeons, to me, represents her resentment for not being able to "fly away" and escape from her humdrum housewife life. She never hits and kills any of them, which is an interesting symbolism of how she never really hits the mark, so to speak, of getting what she wants.
When I first saw Mad Men, when it came out, I really didn't think January Jones was a very good actress. Maybe it had something to do with her one major credit prior to MM being an American Pie sequel and her dating Ashton Kutcher. And after seeing her guest host SNL, I stand by my opinion, but after more analysis of Betty Draper, I'm seeing January Jones come more into the role. Betty is a shallow person, so of course you hire a shallow person/actor to play her. But at Betty's deeper moments, I can't help but picture how a more credible actress might portray her better. And, come one, I know Grace Kelly, and she is no Grace Kelly.