Definitely can cause mitral regurgitation. I believe that, due to the septal hypertrophy and probably some other causes, one of the mitral leaflets is pulled away during systole (see
http://circ.ahajournals.org/content/circulationaha/92/7/1680/F4.large.jpg), resulting in blood going back into the left atrium. It could cause aortic stenosis, but I think that would be more likely in a patient with low preload since that means there's less blood/pressure to push the hypertrophied septum out of the way. This is why diuretics including ACEIs/ARBs are contraindicated in hypertrophy cardiomyopathy. Giving beta-blockers/non-dihydropyridine Ca2+ blockers reduces the heart rate, allowing for more filling, and providing enough preload to push the septum out of the way and minimize the aortic stenosis you were talking about. Mitral regurgitation can still occur though despite this.