Ensure all your tracks are volume normalized from one to the next. You'll be able to make minor adjustments using your DJ mixer, but nothing sounds less professional than a sudden drop in volume or resolution between tracks. Work your set out in advance and run through it a few times before committing it to tape. Building a set on the fly is fine during a live show in a club, but if it's going to be sold as a document that represents you, it's a good idea to take the time to get it right.
Use a condenser microphone on a stand with a pop-screen. Hand-held dynamic microphones have great feedback resistance and are suitable for live work but they possess a narrow frequency range and are susceptible to interference and handling noise. Using a proper microphone is essential to getting a high-quality, professional recording. It's also important to try to record in a quiet space using headphones for monitoring to prevent feedback or echo.
Make a label and design a proper cover for your mix tape -- preferably with photographs. Your music might be great, but you're likely going to be passing it to someone who is handed dozens a day. They're going to look for the discs that obviously have had time and effort put into them. DJs and promoters don't want to waste their time listening to music made by people who need to spend more time working on their material. If your mix tape has an attractive, professional cover, they'll assume you've put the same work into your music.