What you need to look for health test wise depends a little on what crosses the breeder is producing, i.e. whether they're backcrossing to either parent breed or just breeding straight crosses.
Ideally both the cocker and poodle parent would be hip scored with results in single figures. They should both have current (repeated annually) BVA eye tests and the cocker should have a current (repeated every three years) gonioscopy. Both should have had DNA tests (and at least one of them must have tested 'clear') for macrothrombocytopenia and prcd-PRA. The poodle parent should also have had a DNA test for von Willebrand type I. Although vWD is not present in cockers it is possible (though rare) for dogs who are carriers to show some level of symptoms so this test should be done regardless.
If the breeder is breeding (or intending to breed) their crosses back to either parent breed then the list of necessary DNA tests increases for the cocker side. In this case they should also be tested for familial nephropathy, adult onset neuropathy, exercise induced collapse and acral mutilation syndrome.
If they are using cockapoos as either stud dogs or breeding bitches as well as the hip scores and both eye tests they should have all the available DNA tests for both breeds.
The DNA tests can be foregone if there is a record of both that dog's parents having tested clear for each particular condition. In these cases the dog is referred to as "clear by parentage".
Obviously health testing is only a single facet of responsible breeding but it's a good place to start, particularly as (providing the purebred parents are KC registered) you can look up their results on the KC website.