Now if I had only seen this thread a month ago things would be so different. Traded my Suzuki Alto in for a 15 plate Panda 1.2 with 10 miles on clock ( it was registered in March 2015), last month.
I had noticed the flat spot with the car and have never done so many wheel spins in my life pulling away from junctions.
Condolences. You certainly aren't the first person to have got one of the 'problem' cars, and I very much doubt you'll be the last.
Strictly speaking this should be in the Panda forum, but I'm happy to run with it here in the 500 section as the issue seems to affect both cars equally and this is the definitive thread on the subject.
Perhaps surprisingly, we still don't know exactly why some cars seem to be more affected by this issue than others, nor do we know why some folks have been offered a software update, whilst others haven't. Also the effectiveness of the software update is itself highly variable; some folks saying it's transformed the car, and others saying the issue is still there.
With one or two notable exceptions when the issue was first being reported, Fiat have strongly resisted all attempts at rejection by buyers of affected vehicles and noone has, as yet, had the bottle to take it all the way to the wire and take a supplying dealer to Court.
The official line now seems to be that
"this is a characteristic of the car and you'll just have to live with it".
Since first owner buyers have pretty much overwhelmingly been refused rejection, I'd say your chances of getting Fiat or the dealer to take a pre-reg car back willingly are astonishingly small. As you've effectively bought a used car, I think you'll have a very hard time putting together a strong enough case to legally reject; the best that you can hope for is to get a software update that goes at least some way toward sorting out the problem. I don't think the fact you paid by credit card will make any difference as the card issuer will likely follow the official Fiat line and if pressed, they will simply get the car tested and get an independent engineer's report that it is performing correctly as per the manufacturer's specification. They'd also be within their rights to charge you for the engineer's inspection and report, and if you go to Court and lose, you'll have their legal costs to pay as well.
Sorry to sound so negative, but it really is a case of 'buyer beware' with these cars and if you can't get a software update and can't live with the car, pragmatically you'd probably do better to cut your losses and trade it in. You most definitely won't be the first person who has done that.