The tap is the MORAN S15 Harmonica tap, don't you see it?!
Why do you think they show a whole scene of the guy demonstrating this thing? Setup and Payoff!
Caul's phone is being turned into a room microphone. He won't find anything in his phone since it's a special dial-tone entered on the other end of the call.
According to the screenwriter, the wire was in the saxophone, though it was only suggested and not spelled out. Coppola himself has said he didn't know.
Bernie specifically said and demonstrated that the phone of the person being called wouldn't ring. We heard the phone ring the first time and Harry answered it. So...?
So . . . Martin wanted the phone to ring so that Caul would pick up and hear the recording. The recording itself was made on a different attempt when the phone didn't ring.
I think that makes sense. I would go even farther and suggest that Stett hired Moran to surveil Harry, and Moran accepted the job because he is clearly a rival of Harry and got kind of hostile at the party.
Bugging the saxophone also makes sense.
Either of these would, however, require somebody to break into Harry's apartment.
Bugging Harry's glasses wouldn't require a break-in; the woman he slept with could've done it, but that seems a bit of a stretch. She would have to have the technical skills to do it, and have to be fast enough to do it while he sleeps while also stealing the tapes. And how long would such a tiny battery last in an eyeglass transmitter in 1974?
If Harry's just being paranoid and imagining things at the end, then that throws off the whole movie. But a case could be made for that, too, why would they threaten Harry instead of just arrange for him to have an accident?
I just watched this for the first time tonight but i figured he took everything apart except for himself - the glasses definitely stood out. That is where i would imagine it is.