Acer 5720 - cursor/keyboard: applying pressure causes jumping

Solution one: Don't apply pressure to left side of laptop :)
Solution two: Bits of hardware (like your touchpad) plug into the mainboard with thin ribbon connectors. Sounds like this has become loose, or something is shorting against something else. Solution is to take it to bits and reseat the connectors on the mainboard. Not easy to do and I really don't recommend you do it unless you know what you are doing; laptops are so fiddly and difficult to get apart.

If it's in warranty then get Acer to sort it. If not you may want to pay to get it fixed (or go with solution one!).