Some of the characters in my game have blocky looking noses and chins and I was wondering it it's my console causing the issue or the texture problem as I have the game installed to HDD.

it might be a part of the texture problem and installing to the HDD further adds to the texture problem, so uninstall, clear your cache, and play ONLY from the disk and ~POOF in about 30mins of playing textures and proper face shapes magically being to pop up.