I read this and had to create an account to offer up a pilot's perspective and address some of the misconceptions.
First off, yes it will save fuel, and it's pretty easy to see how it works. The most basic concept of flight is that lift must oppose weight. In order to climb, lift must exceed weight. The greater the lift, or the lesser the weight, the faster the climb happens. Makes sense, right? Lift is produced primarily by speed, that is air flowing over the wings. I could spend all day digging into the details of this, but suffice it to say lift is a function of the square of airspeed. Where does speed come from? In an airliner it comes from burning lots of jet fuel. So there is a clear connection between weight and fuel used.
saving weight isn't going to make the engines any more efficient, power settings are the same, so fuel burn will be the same. But given a constant thrust and a constant speed (for this example we'll call it constant. it's actually going to be slightly lower as weight decreases, but with these kinds of weight changes it's not even worth worrying about) there will be a constant lift force. As weight decreases, the climb rate can increase. That's where the real savings are as its high power settings and low altitudes, that means high fuel consumption.
To look at an hypothetical example say we can cut the time to climb by an average of 10 seconds, that's not much at all and it's very possible to achieve. If united makes 1,500 flights per day (mainline united, not counting any united express flights which aren't actually United) that's just over 4 hours of climb time eliminated per day, 1,521 hours saved per year. That doesn't translate directly to a reduction in flight time, but it does allow them to get to altitude quicker where they can pull the power back and burn less fuel. If the difference between cruise and climb fuel flow is 1,500 pounds per hour (its generic guess, across the board covering all types of airplanes) that is 225 gallons per hour, or 342,225 gallons per year. Those are real savings.
Look closer at the weight. You're not only saving 80 pounds for the two pilots. There are typically a few deadheading pilots sitting in the back with their flight bags too. I don't fly for an airline, but I'd imagine United keeps a spare set of performance manuals and maybe even a set of charts in the airplane. You're probably looking at a realistic reduction of around 200 pounds per flight. sure, that's easily offset by one passenger but when you're looking at long term averages it works out.
Next problem, power. Its a non-issue. Every airplane I have ever flown in from single engine piston airplanes to corporate jets have all had either a cigarette lighter or a 110V outlet. Either of which can provide power to an iPad. I seriously doubt United overlooked the issue of how they might power such a device. To take redundancy one step further, I wouldn't doubt that they have put one of those battery powered "charge your iphone on the go" power packs in every airplane. If they have said it will work, and the FAA has agreed, the issues have been addressed.
What I think is the really cool thing is the trickle down effect this is already having. Just a few years ago if you wanted Jeppessen charts, you had to fork out around $2,000 per year, and then spend about 2 hours every 14 days updating the charts. Jeppview (an electronic chart program) been around for a long time now, but used to be around $1200 and wasn't really useful unless you wanted to fly with a laptop. Now you can buy a full set of electronic Jepp charts for $700 a year. My company just went to ipads about a year ago and has saved a ton of money on subscription costs alone. The best news is for private pilots; for around $150 I can buy the charts I need for my personal flying, that's on par with what it would cost to keep up with FAA paper charts, and at the end of the day you have a better product.
I really see this as a win-win for everyone involved except the paper suppliers.
----------
Wrong. Commercial airliners often fly VFR approaches and landings, when conditions allow. If they didn't, air traffic would be stacked up at most major airports. Busy airports like Denver and Dulles rely heavily on VFR to keep the traffic flowing. IFR would dramatically increase the intervals for landings.
They may fly visual approaches, but they are still on an IFR flight plan. It may be splitting hairs, but it isn't the same as flying VFR.