Are you holding this scavenger hunt at whatever location you are having the baby shower? If so, you might want to send teams to collect a list of essential baby items from town (ie. a soother, baby powder, diaper rash cream, nursing pads or a nursing bra), with some fun twists of course. Otherwise I guess you'll be wanting a list of things you can collect in the space that you are for the shower.
a birth certificate
a baby picture
the person whose birthday is closest to the baby's due date
Is this what you had in mind or is there additional information I should be aware of ?