Hide and watch for him to go in the tower.

While investigating the late-night break-ins, the game does not allow you to eavesdrop the conversation and the spy will eventually discover you. A possible workaround for this situation is to make a save outside the radio tower after the spy enters it - if you hear the conversation when you go in, the quest can continue normally. However, the conversation will stop every time the spy has to give a reply. There are two ways to fix this. Firstly, you can pause the game every time the spy has to reply to continue the conversation. If this does not work, you must pickpocket one item from him for every reply. It's best to take weightless items, such as his the 2 codes and 9 9mm cases he is carrying, which can be taken with a Stealth skill of 20. Each item you take will result in the conversation advancing.Another way of advancing the conversation is to enter and exit you pip-boy.

After discovering the break-ins in the control tower you have the option to inform Curtis about it. If you do this the quest will glitch, Curtis will enter the tower as normal but you'll never hear the radio conversation, preventing the quest to be completed. Note: Confirmed on PS3 but it's doubtful that this is a bug. Informing the culprit that you know would most likely cause the quest to go this way. The quest can still be continued by confronting Curtis in the tower.

Using the console, clicking on Curtis, and typing Enable will make the radio say the first sentence. You will have to type Enable every time a sentence ends to hear the entire conversation.

Yeah, this is a notoriously buggy quest. Doing some digging on the quest's http://fallout.wikia.com/wiki/I_Put_a_Spell_on_You summons up the following possibilities:





If you're on PC this sounds like perhaps your best bet: