Maybe I'm just the last person to discover this, but...

You can save time if you're trying to irrigate over long distances, by not having to irrigate around city squares - if they're touching freshwater (water square that gives 2 food) or irrigation anywhere, they become a source of irrigation themselves. Combine this with the fact you can now irrigate diagonally, and it suddenly became a lot easier to bring water from city A to city B.;)

Yes!! I just realized two days ago you can irrigate diagonally. That is a nice change and extremely helpful since you can't use saltwater for irrigation anymore. Much more realistic too - good job on this one Firaxis.