There are tricks to switching keys within a song. There are many ideas that people have explored and written in text books to explain how to do this. However, most of the time it is the songwriters' ears that really make the change work. Where as some artists have a more intellectual approach (Beatles, Steely Dan, etc), the vast majority use their ears and write not knowing what key they are playing in or what chords really go together (by way of knowing theory.) Their honestly isn't a right or wrong way to go about it. Springsteen I am assuming simply uses his ears and heart to write his songs, and in that confidence makes music that comes across very authentic when theory wise it may seem a little confusing.

Theory isn't meant to run your life, but to give you a medium to communicate with other musicians. Write what you think sounds good, even if it doesn't always line up in one key.