Parental inconsistency is terribly prevalent. And really bad. But there are an awful lot of liberal parents out there who blame it for everything wrong about kids because of their misunderstanding that being consistent is more important than doing things right. That's horse shit.
You can't be a consistent ogre to your kids and have everything turn out peaches and cream. It just won't happen that way. You must not only be consistent, but right too.
Let your kids do everything they can survive. Talk to them like they are adults that you love deeply. Try hard to understand how it feels to be them even when they are irrationally upset over some trivia. No, try harder. When they don't know what they want, don't tell them what they want, instead help them set some goals. When they do know what they want, help them learn to achieve their goals. It's not your job to figure out what's best for their lives, it's your job to help them do so for themselves.
You owe your kids a whole lot of time. Not time doing their dishes and laundry, five year olds can do that for themselves and they're made better by the experience. But time teaching them what you know of the world. Time reading together and watching movies. Time pretending to be in another place and era together. Time talking about current events and the world.
A parent who consistently does all those things wrong isn't going to turn out great kids. A parent who consistently turns the TV on for the kids so that he can go do his own thing will have boring, dumb kids who don't know how to function as adults. The problem isn't the TV, it's being ignored.
Consistency isn't everything. A parent who tries to do all the right things but doesn't have the internal resources to make it happen every day is a better parent with luckier kids than the parent who consistently neglects her kids.