How can I make Plants vs. Zombies not pause whenever I switch windows?

With all of PopCap games, it's not possible. Their 'framework' includes pausing when away (ie window not focused). I agree it's inconvenient for these cases where you have to wait until the end of something.

Maybe one could make a tool to fake focus in Windows? It's technically feasible to make a program change the active window of the OS.

Anyway, I think you have to find applications that you can open before PvZ, and that you can use without focus (ie open a webpage on the available desktop space - as @Sorean said, more than one monitor helps).

I can remember someone addressed this with a virtual machine using VMWare.

Not the best option, but it is possible anyway.