1. When striking the bag make sure you are hitting optimally with whatever karada no buki (weapons of the body) you are using, and with the correct angle, depth and trajectory relevant for the target/technique. Therefore, you must fully `understand’ anatomy in the martial arts sense.
2. Don’t `box’, use the wide variety of techniques that karate has, and use them with ichigeki-hissatsu in mind at all times. Seek a finishing blow with every action (do not dwindle your training into sports fighting). Rather, focus specifically for actual self-defence.
3. The heavy bag is where you can impact with full power and develop your body for this, therefore, when doing bag work always seek to maximise your penetration power and effectiveness. Perfect your use of speed and power, and eradicate any unnecessary use of energy.
4. Don’t stand toe to toe with the bag, move around and attack from all angles and distances, and with different timing (both rhythmical and broken).
5. Avoid losing your kihon. Kihon (fundamentals), kata (formal exercises) and kumite (fighting) are one. Therefore, regardless of the training tool (heavy bag, makiwara, etc…) keep your technique. Never change your techniques to suit the tool, rather take the hard road, and make your techniques work!
Another thing Asai Sensei used to say was “hit the bottom of the bag” as he was an avid believer in conditioning of the body. My advice in this regards is to build up slowly, regardless of whatever training you take on. This way you can avoid injuries and make the most of your karate practice.