Partial Soundtrack listing
I went through a YouTube version of the film with Shazam, and came up with these songs from the soundtrack. It's not a complete list, but some may find it helpful.
1 Boo Hoo - Russ Morgan
2 You Got Me - Russ Morgan
3 Boog It - Glenn Miller
4 I'll Be Seeing You - Jo Stafford
5 In Your Eyes - Rational Youth
6 Call Me - Rational Youth
If anyone figures out any of the other songs, especially the jazz tunes, list them below. I'd love to know what they are.