I had this problem before. Although I can't nail down the exact cause, my suspicion is either an aftermarket charger at work, or the very week signal at the same location. My theory is one or the other caused it to go into an over-power state. The reason I attribute it to this is the problem would start as soon as I sat at my desk. It seemed to get really bad when I started using the charger.
The first few times it was just an annoyance. After a few weeks it got progressively worse. Finally it got to the point where it would do it at home and other locations as well, regardless of signal strength. The degradation occurred quickly.
I called Verizon and was lucky enough to reach a helpful person. She quickly identified it as a "known" issue. A hard reset was recommended. I had already done this, so she approved a replacement.
My new (recertified) phone was fine at work for a few weeks. I decided to risk trying the charger again. Within two days I had a few minor episodes of phantom button presses. Needless to say, I got rid of the charger. The problem went away, so I guess I caught it before causing irreversible damage. I've since bought a spare OEM samsung charger. I use it at work regularly. It's now been about 2 months with no problems.
Bottom line is I can not guarantee the work charger alone was the cause. I also used aftermarket chargers at home and in the car with no apparent problem. But, these locations had decent signal strength as well. I was also doing ROM and Kernal changes throughout this time. But, my feeling is the aftermarket work charger combined with low signal quality to damage the old phone.
So, you may want to replace the phone now before it gets worse and buy some spare samsung chargers.