[JPLeRouzic]

Thanks for your answer.

I think the linked article agrees with you that QED is well tested.

Their point (IMO) is that there is one free parameter in QED that was not highlighted as such. There is nothing wrong in free parameters, we know very little of the universe. As far I know there are free parameters in the standard model, but it is clearly stated as such so there is no problem.

https://physics.stackexchange.com/questions/172846/free-para...

[spekcular]

The electron's magnetic moment is not a free parameter that must be determined experimentally. It can be computed from other parameters, as done for example here: https://arxiv.org/abs/hep-ph/0406325.