When Purkey collects his bugs ...
Purkey visits Harry's apartment after the insurance check has been cut and asks if it's ok for him to collect his equiptment.
Willy knew it was there, but Purkey didn't know that Willy knew, did he?
Yes, Purkey knew... eventually.
After Willy negotiated the settlement, he returned to Harry's place but first he stood underneath their spy perch across the street and shouted up to them that the jig was up.
Correct. But apparently Purkey never found out that Willie had known of the bugs all along.
I think Purkey's bugging was all illegal. You can keep someone under surveillance (as from across the street) but not break into their home and install bugging devices, except with a court order, which there's no sign the opposition law firm ever got (and probably would not have been given). At the end Willie even threatens to sue them for their bugging.