Requests and complaints will be filtered through your assistant, and it's often their job to decide which matters to bring to your attention. So, when deciding whom to promote, don't just consider points like seniority or productivity. Of course, you'd like everyone in your department to love you and want to produce for you. But there'll always be a few who don't. With any luck, they may want to produce for your assistant.
Different managers require different types of assistants.
Think about your own management style and define your assistant's role in those terms. Resist the temptation to let your assistant do your job. Define their specific duties at the beginning, and don't dump extra work on them later on. Your assistant's first loyalty should be to you. If you do, they'll hate you for turning them into a snoop, and your subordinates will hate them for being one.