What you are experiencing is relatively common with people in "entry level" positions, including interns. One of the reasons for these 'soft' kinds of positions is to give people good feedback and advice, and let them do what they will with it. It's an opportunity to excel as well, but not everyone "gets it" right away (and some don't get it at all).
What I would recommend is an honest conversation with the employee that cuts directly to the point. This kind of conversation is often not easy to have, especially in a way that doesn't encourage defensiveness and isn't demotivating, but it can be an incredibly valuable skill for someone in your position to develop. Everyone's style is a bit different, but I would suggest something along the lines of, "It seems like you don't seem very interested in your work here."
The conversation could go many different ways, but the key here is that it seems like you are not on the same page. You say he doesn't seem interested, but you don't know whether or not he's actually interested, or if it's something else. It could be that he actually really isn't interested in this job. That's OK - that's actually a large point of having things like internships, so people can figure out if this is something they want to spend years of their life on.
It could also be that he's bored and the lack of challenge makes him not want to try, or that he feels that the work isn't important and he's just putting in his required time. He might not want to work there in the future, but in talking to him you might find that he thinks he does want a similar sort of position in a different company - in which case you can talk with him about how you'd be willing to help him develop the skills and a good reference, which will be invaluable in getting a job at another company.
This person might also be genuinely unaware that he isn't currently on track for a good reference. "I thought I was doing a good job - I got the work done, didn't I?" - that's a really common thing for someone to believe who doesn't understand the idea of "doing the minimum" versus "going above and beyond to excel".
None of this needs to be confrontational or unpleasant. I had a similar conversation with a programmer who just didn't put in the time on a project and seemed like he didn't pay attention in meetings. It turned out he realized during the project that he wanted to be a missionary in a foreign country, and didn't actually want to be a professional programmer anymore. Well jeeze, that rather changed my expectations of him at work! Surprisingly we found a way to get the project done, even with the understanding that this would be possibly his last programming job for years. We focused on how he enjoyed the group and liked learning new things, and he figured the skill could come in handy someday so it turned hurt to schedule time to make things happen.
So, I would strongly suggest you have an honest, friendly conversation with this person that goes beyond the small details (note taking, etc) and focuses on motivation and how he thinks and feels about this internship, and what he plans to do after. I bet you are both on very different pages, and you both might be really surprised by what you find out! If he says he hopes to get a job at the company or wants a good reference for his next job, that's a perfect invitation to talk honestly with him about how he is not on track for that, and make a plan for what he'll need to do to change that. And if you find out he's just passing the time, well then you can safely minimize further investment of you and your company's time and send him on his way. Regardless, you'll have improved some very important leadership and communication skills of your own! Good luck!