Remember that here in Denmark we have one of the best food safety controls in the world, so you can be sure that there are no bacteria in the mussels.
Even though it's a safe food, there's still something you need to be aware of before you can eat the lovely mussels, especially if you choose to pick them yourself at the beach. Here, however, you need to ensure there are no industrial discharges nearby and that you pick them during months with an "r" in them. That is, not in May, June, July, and August.
If there are any growths/algae on the shell, it's not a big deal. You can easily remove them, but they can stay on. It's mostly for aesthetic reasons that you should remove them, and you can do this with a knife.
The next process is to ensure your mussels are alive. Although you bought them in a vacuum-sealed bag in the supermarket, they are still alive and should be when cooked. If they are not alive, you can get sick from eating them. Mussels generally close to protect themselves from predators, so you need to ensure they can close. You do this by tapping the ones that are open a couple of times on the table. They should slowly close (remember they are not fast). Those that do not close should be discarded. Some mussels have a "beard" which you can scrape off with a knife. If there is a hole in/broken shell, they should be discarded. If in doubt, it's always good to remember that mussels that have not opened after cooking should also be discarded.
Pour all the mussels into a colander and rinse them under cold water from a tap.