Mental stability is, of course, a must for serious meditative practices, which are the Real Yoga!
Many serious yoga students feel that they are fit for such practices just because they love Yoga and are very serious about it. Actually, many such students are not so ready. Their mind waivers a lot. They start doing one thing and within 5 to 10 minutes, they want to do something else. For example, they start reading one book, and within few pages they embark upon another good book.
It is good to sit quietly and start one activity and see how long one can sustain it with focus. or, just sit quietly and see whether too many thoughts are shifting.
If there is instability, one should practice just to develop the stability.