I'm prerendering a Angular app for SEO. When I check in the webmaster tool, there are a few hundred 404 and 403 errors. Will this affect my SEO ranking?
No, they only hurt feelings and at most times require you to either go crazy trying to figure it out, or have to explain to a client why they exists.
Either way it is best to know at least why you are getting the errors, if indeed those pages should be showing up.