I would say the things to look out for are reliability, attitude, professionalism and achievements.
When you are junior, reliability and attitude are most important. This means you need to show up on time and stay as long as you are expected to be there. This means you do not create problems for your boss by not filling in timesheets, leaving and not letting him know, taking the day off without prior approval (unless you are genuinely sick and even then you let him know) and doing the tasks you are given on time and as correct as you can make them. It also means, that if other circumstances might prevent you from being on time in a deliverable, that you let him know as soon as possible and what is causing the problem (it is his job to clear roadblocks).
It generally means that you should ask questions rather than make assumptions. And it defintely means you consider what he wants as much more important than anything your peers tell you. It means no off-color jokes. It means no surfing the internet for fun when you have work overdue. It means you communicate with your boss rather than leaving him in the dark. It means you never give flip answers like "I've got it covered" when he asks for status.
It means that you learn first (and have a reputation for delivering the goods) before trying to suggest improvements. Concentrate first and formost on doing the tasks you are given and the freedom to influence the workplace will come after you have a track record.
As you get more experienced, more is expected and more freedom of action is often allowed. Then you need to have a solid record of achievements. You also need to show professional behavior and dress so that he would not be ashamed for a client to be in a meeting with you. It also means that you start to genuine expertise in both the profession you are in and the business domain.
If you want to be a good worker you also tend to go the extra mile and do a bit more than you are tasked to do. Now you have to use judgement and not do anything you were specifically told not to do. As you progress through your career, you will learn what kinds of things are ones that you can show initiative on and what are not. This varies from organization to organization as well and you need to learn to watch and listen and judge what the organizational culture expects form a good worker. However, this is somethign you develop over time, no one expects this from a junior part-time employee before offering a full-time job.
It also means you need to learn to pay at least minimal office politics. Your boss doesn't know you are a good worker if you never let him know what you have done. If you don't communicate your successes, all he will hear about are your failures (and we all have some of those.) It is even better if other people tell him what a good job you are doing. So when you do something for someone outside your immediate boss, make sure they tell him if they are happy with it. Smart employees build up a bank of favors so that when they need one, someone is always willing to help them out because they were helped out first.
Another thing you need to do is leave your personal negative opinions of people at the door. It doesn't matter if you dislike someone on your team, you are expected to work with them and get along. You won't be seen as a good worker if you express a lot of negativelity at work or if you can't work well with anyone not just people your own age or that you like.
Each workplace wil be somewhat differnt is what is expected. The best way to know what your boss wants is to talk to him about it.