Although the Nexus 5's both my wife and I have, are operating flawlessly thus far, I've been monitoring various sources just to stay informed. I've not seen reports of either of the issues reported above.
Being a mass produced product like all other smartphones perhaps you've simply got a defective unit that needs to be replaced. They can't all be perfect, and frankly I'm surprised that I see very few failures. That's a testimony to just how well the various manufacturers are doing.