Picked up an Acer LED LCD the other day. I didn't know it was an extra slim model, but I figured a little extra space doesn't hurt so I decided to keep it. However, when I either move it or adjust the tilt it send waves across the entire display as though I punched it in the screen. Could this to lead to damage to pixels or eventual warping of the display? It really does feel delicate and I can't find any safe place on the bezel to use.
It is a common occurrence. Putting physical pressures on an LCD screen distorts the physical dimensions of the liquid crystals. As long as the distortion goes away and the monitor behaves normally when you don't put pressures on the screen, you are okay.
If you like adjusting your monitor several times a day, I'd consider returning it and getting something with a bit stronger chasis/bezel. It you only have to adjust it occasionally, I wouldn't worry about it like Digerati mentioned. It is semi-normal, though most monitors I have seen you have to press on the bezel pretty hard to really try to torque it to do it over the whole screen.
You're giving up a lot of structural integrity with those extra thin models, especially with a cheap brand like Acer.
Even with higher end models, the desire for thin this and thin that often means less rigidity. Even a sheet of steel will flex and warp with fairly little effort. The different is, the steel is not electrically charged and lit up to see the effects.