1. Continue asking for approval. As the end of your internship nears, it's very tempting to become lazy. Make sure that you stay on top of all assignments and continue to ask for approvals when needed. Make sure you don't assume things are alright, always ask.
2. Watch your spelling. Even after weeks and weeks of interning, we all need to double-check our work and our spelling. Make sure that you use spell check and don't botch company names, executives' names, and/or memos.
3. Be detail-oriented. At this point of your internship, you are expected to know what's going on, and ask the right questions. If you are scheduling meetings or coordinating phone calls, make sure to include all of the attendees first and last names, the companies everyone is from, what the meeting is in regards to, and where/when the meeting is happening, and remember to always check your time zones!
4. Combine your questions. Take very organized notes as you are given assignments -- even towards the end of your internship. This is going to ensure you don't miss anything and you maintain your professionalism. As a task is being assigned, make a list of questions that you have. Don't interrupt your boss with questions. Instead, wait until the assignment is done, and ask all of your questions at one time. If some of the questions are similar, try to condense them into one question.
5. Customize emails. If you are told to send mass emails out to promote a certain event or press release, make sure you pay close attention. If you are sending the same email to multiple people -- the font should stay the same, the size of the font must be consistent, and your email signature shouldn't appear more than once. The person on the other end of the email should not be able to tell that you've been copy/pasting the same text.
6. Voice your ideas. If you have ideas for the brand or company you are interning for, let them be heard. Just make sure that you've identified the appropriate forum to do so. For example, if your company has encouraged you to express ideas during meetings, go ahead. If they haven't mentioned the best way for you to communicate your ideas, try an email. Send a brief email to your internship coordinator and ask for permission to share a few thoughts and ideas. Tell them you'd appreciate their feedback. You don't want to send them a massive list. I suggest coming up with 2-3 great ideas and sending them.
7. Send relevant news articles. If you know your boss is working on a specific project or has a specific initiative for that month, send them any relevant articles you find on the subject. The idea here is to think, "How can I continue to add value?" You don't want to send an article just so you can say you sent an article. You actually want to search for something relevant to send over.
8. Keep your eyes and ears open. Keep a great pulse on what your network of friends and professional contacts is up to. You might be surprised to find that a friend from growing up is interning at a company similar to yours or at a place where there could be a potential partnership. It's important to stay current and always be on the lookout for great opportunities to connect your company with.
9. Ask for a recommendation two weeks before. Two weeks before the end of your internship, you should request a letter of recommendation from your boss or internship coordinator. Tell them that you know they are extremely busy and you wanted to ask them so they had plenty of time before the last day of your internship. Follow up with them about it one week later.
10. Read my book! If you haven't read, ALL WORK NO PAY: Finding An Internship, Building Your Resume, Making Connections, and Gaining Job Experience, you are missing out. I wrote it based on my own experiences as an intern for some of the best companies in the US. You can pick up a copy here.