Genetic algorithms' weaknesses largely boil down to getting stuck in local extrema and premature convergence, which can be resolved by trying different values for parameters like probability of mutation, trying different genetic operators, offspring/parent ratio etc.

Meanwhile you have a whole separate discipline [1] for potential weaknesses on machine learning algorithms. Of course they may win when it comes to interdisciplinary ubiquity in CS, but any algorithm that relies on data assimilation and has little analytic formulation will suffer in robustness.

[1] https://en.wikipedia.org/wiki/Adversarial_machine_learning