On the PTR, currently at least, the Kor'kron are at their most active in the Northern and Southern Barrens. There, you can find settlements, like the ones pictured above, along with a host of other Kor'kron incursions into this once relatively peaceful area.
There are elite mobs, marked on the map by red crosses, which need at least three people to take down, and apparently drop Latent Kor'kron items. At this point, the elites don't seem to tap to anyone, as far as the loot goes at least, but there's also the distinct possibility that I've just been unlucky. You can also have a blast just killing the Kor'kron, although they rarely drop anything at all, let alone anything of use. There are Kor'kron Motivators and other elite mobs within the camps on occasion, too, who drop high quality items.
But for me, the most exciting part of the Kor'kron invasion of the Barrens is the caravans.
It should be stated, so it's clear, that the Horde and the Alliance are both working together here against the Kor'kron. Without wishing to be too spoiler-y, it relates to the warm-up for the raid we know is coming at the end of the expansion, this is the beginning of what will likely be a fair ramp-up of wrongdoing from Garrosh.
Anyhow, these caravans. They are quite the exciting new feature, along the lines of a very basic dynamic event, like those in Guild Wars 2. How it goes down is that an indicator will appear on the map, along with a zone-wide announcement, saying something along the lines of "A supply caravan needs to be escorted from Crossroads to Far Watch Point". You then need to head to where that caravan is, it'll be on the map as you see to the right, and keep it safe from marauding Kor'kron. These are level 90 mobs, so caution would definitely be advised for any lower level players who come across them.
Safely escorting the caravan to its destination awards Surplus Supplies, which contains items such as Kor'kron Meat, Kor'kron Oil, Kor'kron Stone, and Kor'kron Lumber. It's unclear right now whether players actually have to have killed Kor'kron mobs which were attacking the caravan, hit the mobs, or just have to be in the area, but all the same-faction people I chatted to were getting the supply boxes.
On the topic of caravans, there are also Overturned Kor'kron caravans, indicated on the map by the blue-gray symbol in the map shot above, in the center. Wowhead postulated that they were a way to disrupt the Kor'kron, but it is very unclear at the moment. They don't seem to do anything but sit there!