Having exactly the same problems - one area of my house (where I will be using the mini most) I am just completely unable get signal from the mini. My iPhone 4S and 1st gen iPad work no problem.
When I do move to a location where I am able to connect to the wifi, the mini seems considerably weaker (only 1 bar compared to the 1st gens/4S's 3 bars). Performing speed tests on my 4S compared to my mini, I am able to get approx 30mbps download compared to 16mbps on the mini. The performance is even worse when it is being held.
I am 100% certain that this is a hardware issue. I have taken all the necessary steps, resetting the router, resetting network settings etc (I am running 6.0.2). I have now had 2 replacement iPad mini's from my original purchase, and the problem has been there for every single one. Surely I can't have been given 3 dud iPad's?
I have decided today that enough is enough - I am taking the iPad back and going to get myself a Nexus.