As you may be aware, a new SI system is likely to be adopted in November 2018 (see https://www.nist.gov/si-redefinition/kilogram-introduction).
Whilst the speed of light remains a fixed quantity and hence $\epsilon_0 \mu_0$ remains fixed, the definition of the kg and Ampere will change such that $\mu_0$ will have an experimental uncertainty.
What is the current level of that uncertainty?
I note Uncertainty of permittivity of vacuum, which is clearly linked. But I also note that all of the answers there are based on the soon to be superseded current system in which there is no uncertainty in $\mu_0$ or $\epsilon_0$ and are therefore about to become incorrect!