Just off the top of my head, I recall that gape worms can be checked by sticking something like a q-tip (carefully) into the duck's throat - like swabbing for a strep culture. Apparently parts of the worms will detach and you can see them. Chronic coughing with head shaking can be a symptom, too.
Looking at Storey's Guide, Holderread indicates that worming just to worm them has long term negative effects on the ducks, as it can reduce their natural immunity.
He also indicates that the best, sure way to know is a fecal sample to the vet.
Other symptoms are weight loss, reduced egg production, eating more without gaining weight, weakness, diarrhea. A bad infestation can be fatal.
Clean water, no overcrowding, no standing water and quarantine of new birds are recommended for prevention.
He mentions some people using diatomaceous earth as a treatment, in addition to worming medication.