Remember to start thinking about the fact that we have one of the best food safety regulations here in Denmark, so you can be sure there are no bacteria in the mussels.
Although it is a safe food, there are still some things you need to be aware of before eating these delicious mussels, especially if you choose to pick them at the beach yourself. Ensure there is no industrial discharge nearby and that you collect them in months that have an "r" in them. That means not in May, June, July, and August.
If there are any growths/algae on the shell, it's not a big deal. You can remove them, but they can stay. It's mostly for aesthetic reasons that you should remove them, and you can do it with a knife.
The next step is to ensure that your mussels are alive. Even if you bought them in a vacuum pack in the supermarket, they are still alive and should be when cooked. If they are not alive, you could 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 open ones a few times on the table. They will slowly close (remember, they are not fast). Discard those that do not close. Some mussels have a "beard" that you can scrape off with a knife. Discard those with a hole in or damaged shell. When in doubt, you can always go by 'better safe than sorry,' but remember to discard any mussels that do not open after cooking.
Pour all the mussels into a colander and rinse them under cold water from the tap.