Revealing mistake: When closing the portals that spawn enemies using silver, Ash will stand there during the in-game cut scene as the portal shuts and do nothing. If an enemy spawns in the portal just before or as it's closing, it will start attacking Ash during the cut scene, and Ash just stands there taking hits until you're able to control him again.
Continuity mistake: In the opening cinematic, Ash is dressed up and just fine, with no damage to his clothing and a complete blue shirt on. During that scene, he shoots one enemy with his shotgun and then goes outside before gameplay starts. Now suddenly Ash's shirt is all ripped to shreds, with parts of his chest showing and a sleeve fully missing. However, he hasn't done anything yet that would cause his clothing to be damaged. He shoots one guy and walks outside.