*** EDIT: THIS POST IS INCORRECT – THE PROBLEM DOES APPEAR TO LIE WITH S2Member **
Ok this appears to actually be much further reaching than S2Member.
S2Member does most definitely produce this error when activated at the same time as BP 1.6 but so do the plugins ContactForm7 and AdRotate so I think the focus is back on BP 1.6 as the thing needing a fix.
You should be given a crop screen after uploading your avatar where you can drag a square over the portion of the image you’d like to use.
If this is not the case it sounds like an issue with the theme you’re using – you’re best getting in touch with the people that developed it. Alternatively you can activate the default buddypress theme and try to customise that to suit your needs.