When escaping the goons at the beginning of the game and trying to get to the street level, George has to cross a pipe which breaks off, preventing Anna from following. Just before he crosses, Anna is in my inventory, but as soon as he gets to the other side, she isn't. I know I will need her to help me a little later, but I can't use her if she isn't there. Has anyone else run across this apparent glitch?

IIRC she doesn't appear in your inventory, because at the moment she is in place from where she can't help George. She will reappear into your inventory once she in actual position to help you.