As a PhD student pursuing an academic career (but optionally a career in industry), what should I do do to get the most of a 10-week internship at a research lab?
Things I've thought of: talking with people (networking); attending talk/seminar (new ideas); giving a talk (get people to know you).
What other things can/should be done?
First of all, good for you in getting the internship. Now that you're there, some suggestions for what to do, broadly and specifically:
Meet people with similar backgrounds to yourself. Find out what they do, what skills they value, what skills they wish they had.
If you're in a large company, talk to people in other parts of the business, see what they do. You may find positions in other parts of the company that interest you that you weren't even aware of.
If you're in a large company, talk to managers, see what they desire in people like you. They'll already be slightly impressed that you thought to talk to them. Learn what they do, what skills they like. It can help you guide your career later on.
Learn new skills & hone old ones. This is a good time to see which of your skills are marketable and which aren't. Get really good at the marketable ones.
Use the opportunity to reach out to people in similar positions at different companies and see what they're doing. If you don't know people at other companies, ask around; your new coworkers should have friends they can put you in phone/email contact with, and you can take it from there.
Above all, try to do a really good job. Internships can often lead to full-time employment, so you want to impress.