The way you finish your internship will be, in the main how you are remembered – it will be your lasting legacy.
Finish writing up your work so that anyone who carries on your work or has to support what you have done has all they need from you. Leave it tidy and professional.
Ask for feedback if a formal internship review has not already been planned. If your internship went well this will be a good opportunity to really benefit from performance appraisal and reflection, if it went badly you have nothing to loose by not being honest – although never resort to rudeness or insults. Receiving and discussing your performance effectively is a valuable skill for the future and this is a good opportunity to learn how it is done in your company.
In what ways have you met expectations?
In what ways have you fallen short of expectations?
Which of your behaviours were appreciated?
Which of your behaviours could have been better?
How has what you have done and learned aligned with your upfront objectives? If there is a gap does it merit discussing?
Is it appropriate to offer to support your work after you have finished? Perhaps finishing off a piece of work in your own time and then sending it in. These can again create a very good impression BUT you must deliver when you say you will or your credibility and impression will significantly fall.
Now is a good time to ask about future work opportunities but ask this in a very positive way starting with how much you have enjoyed working in the company and how much you have learnt and grown. Don't be too boastful about what you can do for the company but you could hint at it. If you want to work for the company why not ask!