I'm also unsure about the blurriness because the thing about a digital signal, you either get the signal or don't. Digital is not like analog because if an analog signal is within tolerance (+/- x volts), it'll display something albeit ghostly, flickery, grainy. Digital is either on or off.
There are plenty of posts...especially from me...about slow cable boxes. Just search lag or sluggish in the TV Forum. The slowness eventually disappears but I don't know why.
Batteries would not be an issue. Every morning for the past month, Contour has been warning the batteries in my remote are low. Right now, it's at 6%...but still works with no lag. I just want to get to the point of the batteries becoming completely depleted...and I also don't know why.