I have seen First Contact easily a hundred times... it might have it's plot holes (I enjoy watching RLM's review as much as the film itself) but it's just so entertaining... yet I only just noticed this.
It's not a mistake, but it is hilarious. Just watch the old man in the background during the scene where Riker, Troi, and Cochran first meet... and when Cochran reactivates the jukebox. LOL, this gut reaches across the table for a drink and takes a mighty swig. He is so funny!