The singer surname/last name is "Springsteen", or is it?
I tried to watch the video, altough I had to stop because I would wake up
everyone else around house, he he.
Indeed, I agree with you, he doesn´t voices the "and" (on the 2nd line).
Sometimes in songs the singer kinda "eat" a word (to our ears, at least, since we aren´t used to some soft sounds).
It´s not the case, since in watching the clip I was "reading" his expression, reading his lips (a thing that I asked a teacher of mine once, why she didn´t let us to see the images in a certain test, she said it wasn´t about the sound...we could read the lips of the character).
Now, I can think of the following explanation: it´s that the normal thing after the first line would be the use of "and" but it´s music, it perhaps would lose the "flow", the tempo of the music. So, the lyrics is that, but the singing of it is a bit different, and maybe if you try to sing-song literally by the lyrics you won´t keep up with it. Anyway, it´s music, and this doesn´t ruin the general sense (to the music fan).
Philadelphia takes a capital "P" in the beggining of the word.
Hope it helps, and let´s wait more comments.