Apple didn't just change the policy on AppleCare because of any concerns they have with New iPad. AppleCare + was introduced last November to put a real policy in place to stop giving free replacements for damaged products. One can purchase AppleCare + at the time of purchase, or within 30 days, but if you've taken deliver of your device, it does require taking your unit to an Apple Store to have them look it over to ensure there is no damage, which is actually quite reasonable.
Now, to your issues. If you're not happy, return it and get a new one. Having pushed my new iPad hard, I have no heating issues. And my Wifi connection is no less than my iPad 2, which I just sold, but there is another iPad 2 in our houselhold and they both get solid, consisten connections. The router in my office is more than 100 feet from my desk and I get a solid connection at the office as well. I haven't been to Starbucks with my iPad yet, but I'm sure I'll get reception equal to my iPad 2, which was acceptable, but by no means anywhere near the speed I get at home. I can download a magazine from Zinio at home in a couple minutes, where it takes about 15 minutes to download a magazine at Sbucks. Now, my new iPad as well as out iPad 2 are in cases. Always have been, so I'm not holding it directly in my hands, but then I never had any issues with the Antenna on either of our iPhone 4 phones when it was reported many did.
Also, I'm at home and sitting about 25 feet from my router. I performed a speedtest on both New iPad and iPhone 4. They were both pretty identical with Download of 9.17 Mbps and Upoad of 1.78 Mbps on iPad, and Download of 9.04 Mbps and Upload of 1.84 Mbps on iPhone 4. Again that's at least 25 feet from my router and we have metal studded walls in our condo.