Not so much, really. Any field that’s been run over with farm machinery for a few decades will pose no problems for a pivot, barring steep hills. You might have a rockpile or fenceline that needs cleaning up, but wholesale terrain changes to allow the pivot to run would be very rare.
Um, actually, no there’s not. Liberal is just across the state line in Kansas. We don’t let them damn Yankees in Oklahoma. 
As far as the ends of the fields is concerned, usually the farmer will plant something in them that doesn’t require irrigation. Here in southwest OK, that typically means wheat or cotton.
Personally, I’ve always wondered why they lay them out in a square pattern, rather than hexagonal. I’m sure that the land in the corners is put to some use, but it can’t be as profitable as the irrigated land (else they wouldn’t bother with the irrigation at all). And a hexagonal pattern would have much less wasted corner space. Or they could even have irrigation rigs of varying sizes, to cover the cropland as efficently as desired.
The land is surveyed in squares. No one’s going to want to put up a pivot that overlaps on several chunks of land owned by different people. Still, there are different sized pivots. In the pic in the OP, most of them are quarter section pivots, but there are a few that cover a whole section, and some smaller ones as well.
A lot of them are. I thought I saw a hexagonal pattern at one of the previous links, but I can’t find it now–I must have seen it somewhere else.
Duke of Rat hit the point I was going to make, but I’ll elaborate anyway. Around here you see a lot of pivots and many of them are on land that’s not even close to level. A friend of mine has a quarter-section pivot set up, and I’ll bet there’s a 30-foot difference in elevation between the highest and lowest points it crosses.
As for why they don’t worry about filling in the corners, or tiling in a hex pattern, the Southwest US is very big and there is lots of land out there. It’s cheap enough that the costs of filling in the corners aren’t worth it.
A life-sized game of Connect Four that got way out of hand.
Oh yeah! You’re right, Liberal is just across the border. It didn’t show up like that on Google Earth, where I saw it.
Mind you, that stretch of Oklahoma that is squeezed between Texas, Colorado, New Mexico, and Kansas looks like it might be a bit of a no-man’s-land really. Perhaps a contentious part of the land that’s been fought over in the past?
The Oklahoma Panhandle was once known as No Man’s Land, FWIW.
That was a damned good guess of mine, then.
Ed Zachery. The land is cheap because you can’t grow much of anything on it unless you irrigate it. Production is then limited by how much you can afford to irrigate, not how much you can purchase.
The corners are good for grazing stock, storing impliments, and charging hunters (pheasant, dove, etc.) hunters admission.
Occassionally I have seen senter pivot setups where other means were used to fill in the corners. Another interesting irrigation methode is a giant rainbird sprinkler with onboard pump that travels down a ditch in the middle of the field. Been 10 or 15 years since I’ve seen one of those working though, so maybe they went out of fashion.
Then how’d Oral Roberts build that university in Tulsa?
I can’t find the brochure, but I got some info a couple of years ago on a pivot irrigation system that could fill in the corners of a square field. If had basically a water jet on the end with a valve that changed the water flow based on the angle of the pivot. It takes some careful adjustment, but you can set it so that when the pivot touches the center of one side of the square, the jet isn’t squirting at all. Then, 45 degrees later, it’s at full power, squirting water out to the corner.
They’ve got linear systems too but they appear to require a greater degree of monitoring and, likely, effort.
I imagine the choice between pivot and linear is dependent on which is your greater cost… land or water.
A little determined Googling reveals something called a MAXfield corner system:
http://www.zimmatic.com/zim_agsysystem_MAXfield.asp
Here’s a web page containing far more information than you ever wanted to know about center pivor irrigation systems and corner end guns:
http://www.bae.ncsu.edu/programs/extension/evans/ebae-91-151.html
Yeah, you can use those end guns to fill in corners, but on fields I’ve seen with them, they’re just turned on full blast all the time, so as to just give a bigger circle.