Dean Takahashi has a great article at VentureBeat about the problems Microsoft experienced with the Red Ring of Death, what caused it, and a how it went about trying to fix the problems.

Reading the article, it seems that the problems boiled down to rushed production, improper test setup, a software mentality that problems can be fixed after release with patches, and insufficient experience with producing consumer electronics. All of this was was later made worse by the corporate "we must deny problems" mentality, until such time that Microsoft was forced to extend the warranty and acknowledge the problems.

To conclude, the video game industry has never seen a consumer problem as bad as the “red rings of death” and the size of the $1.15 billion charge stands as one of the biggest liability glitches in consumer electronics history. How Microsoft handled the flaw may provide a lesson for all modern electronics companies; that is, if you are going to promote the hell out of something, it better work the way you say it does and you better have a strong customer support and engineering debugging team to back it up.

Excellent article, well worth a read especially for anyone bringing a product to mass market.