I just test drive one a copule of day ago with a good friend of mine (manager of a Mazda dealership).
Road condition: Sunny day and the road was completely dry (no rain on the past 2 days)
Speed on some of the corner: About 60-70 mph (just an estimate)
(Of course I won't look at the mph, just focus on the road, traffic and rpm. AND IT'S AT YOUR OWN RISK)
I don't feel any spinning on wheels.
Maybe the spinning of the tires are just that they're still new or not "season" yet.
Anyhow, it's a good car and I should say is one of the best car around in the market with this price. Worth buying.
On personal opinion, the car looks better than on the picture and the back seats space are not as tight as I expected (but I don't recommend anyone to seat at the back for long ride)
I have not driven the RX-7 but my friend owned both (RX-7 & RX-8) said both have its own pros and cons (haven't really ask him what he meant, sorry)
As for the engine, there shouldn't be any problem or they have not discovered any yet. I believe there might be just some small problems (on other parts, not the engine, just like the recall on the Mazda 6's foglight)
My recommend is: wait for 1/2 a year before buying it, so there'll be more reviews on this car. (not the one by magazine). If you can't wait, go to the dealer and put a deposit to reserve the car. Larger dealership would have more option and color for RX-8 to choose from comparing to the smaller size dealer.
Please think twice before getting an automatic, I think you'll loss the "original" feel of the car.
All of these are my personal opinion. everyone's opinion are vary.