In the third picture, if you look in the bottom left and right corners, you can see a sudden colour change along the lines where the original picture's content ended. On the right, for example, the original cloud is sort of yellowish, then it suddenly becomes a more neutral grey along a diagonal line.
In the sky it's harder to tell, but it's still there too.
Except those aren't actually the original picture. That's the picture with the trash already removed.
Not that I'm saying Gimp can't do as good of a job. It's exactly the same technology based on the same research. But I am saying that blog post is a tad dishonest.
Probably not. There are a number of image inpainting, texture synthesis, and reconstruction algorithms that can be applied, with different behaviors regarding noise, color correction, detail scale, handling of regularity/irregularity, temporal coherence, run time, etc.
GIMP's Resynthesizer is based on a 2005 PhD thesis, while the Photoshop thing is probably based on a 2009 SIGGRAPH paper.
In the sky it's harder to tell, but it's still there too.