Chosen Solution

The trackpad on my Macbook suddenly stopped responding properly, when I move my finger the cursor stops intermittently. I found two workarounds that might give some clues:

  1. if I apply even just light pressure under the trackpad the cursor moves as it should,
  2. it also works if I unplug the power source, ie. in battery mode! (not ideal, since my battery is seriously bad) Any ideas what might cause this problem?

It sounds like you have a double whammy here. If your Battery is going it could be pressing on the trackpad from below, often times the battery swells up. I would test it using CoconutBattery Post a snapshot of the main window here so we can see how it looks Adding images to an existing question. If needed replace it and you still may need to replace the trackpad and its cable if they got damaged. MacBook Pro 15" Unibody Early 2011 Trackpad Replacement which is the same process for your system. And here’s the battery info MacBook Pro 15" Unibody Mid 2010 Battery Replacement

try SMC and PRAM resets. those solve most software related Mac problems. if SMC and PRAM resets don’t work then you might have to replace the trackpad. How to reset the System Management Controller (SMC) on your MacReset NVRAM or PRAM on your MacMacBook Pro 15" Unibody (Mid 2009-Mid 2012) Trackpad