FIXED!!!!(Returned) I was another victim of almost non-existent wifi on my Christmas present iPad4, black 32g. Here's what I did.
At first I worried about my home network. I have a Linksys router that's a few years old but has worked fine with my PC, laptops, iPod, and assorted Android phones. With the new iPad if I was not sitting at the desk, within 18 inches of the router, I could not get a good signal. If I backed away (still in a direct line of sight) eight to ten feet, I would lose signal all together. Other devices connect throughout the home, unattached shop and can see neighboring networks.
I work for the local municipality. Took the iPad to work and checked reception there. Dismal. Not my older network.
THANK YOU to everyone here for the ideas and tips. But I would suggest that once you've deterined that your other devices are connecting and functioning properly on the network(s) you use... return the iPad immediately. I was lucky and through Bestbuy(black Friday) I had 60 days to sort through a lot of the info in this thread first.
I had to wait a few days(out of stock), but the replacement works flawlessly!!! Get rid of your piece of your junk paperweight if you got stuck with a bad one. The replacement has no "hand hold" issues and at times better network searching capabilities than the former. It is night to sun-shiny day!
Both machines had/have serial numbers starting with "DM". And for what it's worth, the associate I dealth with at Bestbuy seemed to know better than to argue about the wifi issues. Good luck everyone!