Should we interpret a problematic hiring process as a red flag about the company in general? Any stories showing the opposite (i.e. poor hiring process at a great company to work for)?
Companies have areas of expertise and areas of weakness - their hiring process might be a weakness, but that doesn't necessarily mean that working for the company will be all bad.
That said, the hiring process is a view into the company culture, and if the view of the culture you get is not good, then working for the company is probably not going to be great.