my last rig had a gtx 260 and don't remember that happening on any mass effect games , my new rig has a gtx 1080 , I can ramp up everything on games such as gta v and witcher 3 , that said , I have been revisiting some old games such as dragons age and had face tearing.
I have done a bit of googling and the problems seem to be caused by the nvidea physx part of the drivers , the ones you get now are too advanced for older games.
scroll down this page link
click here you will see somebody saying click this link to get an old copy of the PhysX part of the driver program , note , I am not telling you to do it the final choice is yours , I don't know what will happen if you have an old and new PhysX component installed.... all I did was find it for you .
btw witcher 1 and 2 gave me face tear as well