mini cooper hesitation on acceleration

It could, but it's very doubtful - the CVT was the worst thing to happen for the Mini, and it is otherwise impeccably reliable with zero true mechanical flaws.

Thanks for your response. I'm getting used to it. It's now only a problem trying to get out of the way of the Big Rigs!

the CVT does have a sport mode like the BMWs which is activated by pushing the shifter sideways, this will sharpen the shift pattern a little in a pinch, also if your battery is original, it really wouldnt hurt to replace it with a new correctly sized unit and have a workshop re adapt the cvt shift points. this can also make a notable difference

You should also remember that your throttle body is attached to the accelerator via drive by wire. Which causes hesitation in the throttle response.

The CVT takes getting used to for sure. For optimum start start in 1 (Sport side) take to 5500 RPM go to normal then back to S quickly / Best jump I had from my CVT before it died at 150k miles

I hope I don't have to get out of the way of anything....... if I do.....I'm toast!

Make sure you torque the plugs. Most have a crush ring. It's easy to tell. Simply place the spark plug wrench on the plug and try unscrewing it out with only the extension. I could simply turn two of mine by hand with no socket wrench because they were so loose. Once tightened no more skipping!