Maybe a dodgy mussel is one that is dead (shell open). I agree never eat a dead marine mollusk, as they spoil very quickly (and you do not know how long they were deceased). If you tap them they will close the shell if still alive.

Mussels (cultured) in the market are pretty safe. Safe also are oysters, which are harvested and held in certified water areas to cleanse any potentially bad stuff.

As for wild mussels (rare as they may be),and soft shelled clams, one should beware. Though areas are closed, some bad folks still harvest and sell them. There is mostly no certification process for sellers. If you harvest them yourself, or know where they come from...this limits the risk. If they are depurated no problem also.

A main health hazards are fecal cholorform, from animal waste. Residential, recreational and agricultural run off is normally the source, which is injested by the clam. You normally get flu like symptoms, that will pass (no pun intended). Some folks are less bothered by exposure (I suspect like the folks in Mexico who can drink local water without impact). No long term concerns, except if your immune system is already weak.

Paralytic shellfish poisoning (PSP, or red tide) is a potent neurotoxin. It accumulates in prone areas during warm periods. You will be hospitalized and if you survive, there are no long-term impacts.

However, there are also a couple of other naturally occurring toxins (for example Domoic acid, also a neurotoxin ) that can cause long term brain damage.