There are two possible scenarios in play here:
The first is less likely, but does happen. It's possible that a nearby electromagnetic field is causing the buttons to engage, and this can happen when powered items are placed near the buttons themselves.
The other is more common, where the button - for whatever reason - seems to connect. This could be do to either a hardware malfunction beyond the buttons, or the buttons themselves due to the distance between the button (or faceplate, since they're "touch buttons") and the connection, and has little to do with user error in most instances.
I would recommend having the unit serviced so that the issue is fixed.
I recently bought a Samsung P2370 (not HD) and it has been working great. However, a problem with the touchscreen buttons has developed where the monitor will turn off by itself as if the buttons are being continually pushed. Sometimes if the menu is open, it will scroll down, up, or into menus and the respective button will flash, again, as if being used.
When the monitor turns itself off and I turn it back on, it usually turns itself off immediately. I struggle with it for a while (repeatedly turning it back on while it seems quite adamant about staying off, much to my chagrin), and eventually it stays on.
I don't suppose you know the source of the problem, or any surefire methods of convincing the monitor to do its job without it's wonderful attitude?
My system specs, if they are important:
The monitor is at 1920x1080
I'm using Windows 7, 64-bit
Nvidia GeForce GTX260