Well, there's no guarantee, but the same team that worked on the "Trinity" Xbox 360 Slim unit is behind the hardware in Xbox One, and that's a good thing.
I guess I've been lucky: I didn't buy an Xbox 360 until I signed on with the original Tom's Games back in 2007, and so far I have the same unit, red-ring free. It doesn't seem to like Minecraft: Xbox 360 Edition in split-screen mode, but I have no hardware horror stories to tell. Unfortunately, I can't speak for everyone. The Red Ring of Death is not something consumers want to see or hear about, ever, and neither does Microsoft, especially in the next-generation hardware.
Microsoft Studios boss Phil Spencer told Edge Magazine that the team that built the latest Xbox 360 Slim "Trinity" model is the same team behind the new Xbox One. He said this team's work so far has inspired confidence in the reliability and quality of the new console. Of course, he's going to say that given a new product is about to launch later this year. But the failure rate with Trinity seems minute, if at all, compared to the early days.
"The last Xbox was Trinity [Xbox 360 Slim] and our success rate on Trinity was very high," Spencer told the magazine. "We learned a ton from the 360 launch and we took care of our customers with the extended warranty, but I think Trinity is telling."
Spenser recently told the magazine that Xbox One isn't backwards compatible because Microsoft wanted to be in a "forward-looking position," to release a device that will last for the next ten years. Because of this, backwards compatibility had to be removed from the feature list. Still, that doesn't mean Xbox 360 games can't be streamed in the future. If Sony can do it, Microsoft could presumably do it as well.
He also revealed a little insight into the console's DRM, stating that games will be "locked" to each owners' profile. Of course, that could seriously affect the secondary used games market, and he admitted that Microsoft will release specifics on how it will address this market at a later date.
"We think, actually, that having the content that’s yours go with you is an important thing," he told the magazine. "You could have multiple Xbox Ones, your content is yours on every one of them, and it doesn’t require that you carry discs back and forth. The disc becomes a means of distributing the bits back and forth but the content is locked to you."
"I think the whole idea of a secondary market is important and it’ll be important in the next generation and we’ve designed [Xbox One] with that in mind from the beginning," he added.