I don't think the foot thing would really work that well. It would only detect where your foot hit the ground. So unless you are going to shuffle your feet like a human "choo-choo" I don't see how you are going to get much out of it. It would be in contact with the ground for so little time that it would probably be worthless. But if you did want to persue this type of covert detector I wonder if it might not be better to just create a coil that could be tacked to the bottom of your shoe? A small 1/2" deep coil placed on your heel (like the heel of a boot) probably wouldn't be too bad. Then you'd run the wires up your leg and into a standard MD control box. It's just an idea.
As for digging discretely, I've thought before about how I would do this in a public area. I would take a picnic basket and make the bottom be a trap door. Then I'd set it over the area and dig the plug inside of it. People would think that you were rooting around for something in the basket. Be sure to take a giant blanket with you and spread it out. You could also use a handheld detector over top of the blanket to find your next target to dig. If you act like you are doing something normal then people won't pay any attention to you at all. Having a "partner in crime" to enjoy your picnic with would help as well. Basically, you'd look like two people having a picnic and you'd end up scooting your blanket by 5' or so every few minutes. You'd cover the area one blanket at a time until you had found whatever you were looking for. It is certainly not foolproof but it might do the trick depending on where and what you are digging.
Going back to the homemade metal detector, I've seen that one before. I remember reading somewhere that doesn't actually work very well and can be hard to tune correctly. The nice thing about it is that you don't need any electronics experience to create one. But if you do have electronics experience, there are plenty of other schematics out there on the web for detectors that would likely work better than the calculator kind.