Just from my observations, I see the same shows cary from week to week. I think part of this is these variable rate encoders, part of what you end up with PQ wise depends on everything going on with that TP at the same time. Just my SWAG.
Ive come to the point where I do not get my panties in a bunch over HD broadcast PQ. Some shows even on good channels are shot to look like crap. I make sure I have good gear, record as much OTA as possible and save my PQ gripes for blu-rays
As far as checking what the box is doing, ive you have any decent AVR or just hit the info button on your tv remote, it will tell you incoming resolution.
My Denon reports 1080i/60 ycbcr 444 from the Hopper.