Is autocorrelation of residuals a problem in machine learning?
Yes, autocorrelation in residuals is a problem, but this is essentially because it is a clear illustration that there was more learnable information in the process you are modelling but your model missed it.
In the unlikely event that you have two equally performant models but one shows significant autocorrelation (you can test for this using the Durbin-Watson test as suggested in Noah Weber’s answer), this suggests neither model is working as well as we might hope (the autocorrelated model has failed to predict some predictable patterns and the other model is failing in some other way as its predictive power isn’t any better).
If you have two models that have different residuals but both are beating a naïve baseline, you’ve probably got models that will ensemble well.