Errors are important to know about. If you don't deal with correcting the problem, you have a high chance of a corrupted save. It is a good thing that they appear the way they do. You should not be getting any errors if you have your have properly set up.The console should not obstruct interaction with the game, even in a broken game state. This prevents further interaction with the game for errors which the player may not care about and renders further testing impossible for errors the player does care about.
You can close the console unless you are getting non-stop errors, in which case, the game isn't going to work anyhow." You should not be getting any errors if you have your have properly set up." Agree, however if the application is still running, why does the console block interaction with the application other than the console? Additionally if the errors could result in a corrupted save why don't they crash the game? or take you to the main menu? Consoles are expected to show errors, not prevent them.