IMHO you have nothing to worry about. You are simply showing an excerpt of the longer page with a direct link to the full content. The search engines will figure that out ok.
In this example the "About" content is going to be only one small part of the overall homepage content. The important thing is to make sure that is is not mistaken as the most important part of the homepage content by utilising H1s, H2s etc to structure the page.
Finally see the full guidelines from Google on Duplicate content here for further reading http://support.google.com/webmasters/bin/answer.py?hl=en&answer=66359