Teaching the "leave it" command is a great idea. Our guys know this well and for the most part they listen (unless of course they have something of extremely high value that they've discovered).
Bring treats on your walks (high value treats) and each time she picks up something she shouldn't, give a firm "Leave it" and show her the treat. If she drops whatever the undesired object is, praise her and give her the treat. You may have to "help" her get the object out of her mouth at first but if she knows a treat is coming, this may work. It worked for us
