Not really a problem, relativistic effects are negligible at the very low accelerations MOND is about. Should MOND work with galaxies, a theory that say "if the force is less than a threshold, use MOND, otherwise, use general relativity" is not pretty, but good enough to match the observations, and that's the important part.
There are more elegant ways of doing it (ex: TeVeS), but before looking at the best way to reconcile general relativity and MOND, something we know is possible, it is important to make sure that MOND works at the scales it is supposed to work with. Currently, it doesn't, but dark matter doesn't either. More research is needed, as they say.
Disclaimer: Personal Opinion:
Personally, I don't think MOND will be the solution. But I don't think it's going to be dark matter either.
1. We don't have a a way to unify relativity and quantum mechanics yet 2. Dark matter and MOND effects show up at extremely low accelerations.
I have a hunch it's going to need a theory of quantum gravity to properly solve this.
A century ago, quantum mechanics was initially formalized to explain the uktraviolet catastrophe of blackbody emissions.
The difference between the classical emissions curve and the quantum based emissions curbe is very similar to the correction factor applied by MOND. I don't think that's a coincidence.