In the beginning, the officials at the prison figure out that the ambulance that is carrying Tom Bishop is involved in a escape plot. They apparently figure out by seeing a prisoner blow bubble gum which we see Tom giving him when he is first looking for Elizabeth's cell. Try as I might I cant figure out how the bubble gum chewing prisoner was the link to the discovery of the plot.
The prisoner was seriously mistreated, and certainly wouldn't have been given bubble gum by anyone except for the outside doctors. Since they had kept tabs on everyone except Tom (thinking he was dead), the most logical conclusion was that he, or at the very least someone, was poking around where they didn't belong.
The man could either get a reward from the guards for turning Tom in, or get a reward (the gum) from Tom for keeping silent. Bubble gum would've been a very special treat.
Also, it was sort of Tom's training. Nathan tells him at one point "most of the time all you need is a stick of gum, a pocket knife and a smile."
The gum chewing prisoner is one hint, but others do exist also. The doctors nervously looking at the security cameras screens would be an example. Also the guards had to be cautious after power surge had happened.
We're to believe that the same people that can't keep their prison locked down or even powered up somehow also have the sherlockian brilliance to assume that there's an escape from someone having gum.
I'm surprised that no one has mentioned that it was CHEWING gum, not bubble gum. That's what we call in the tradecraft "a goof". Obviously done for aesthetic reasons as Wrigley's is much more identifiable as gum visually, but still...