You are especially likely to see sharp lines between the 8x8 squares, an artifact often called blocking.
All true, but keep in mind that this isn't apparent to most observers. The quantization errors, depending on quality setting, produce only small differences in apparent value between adjacent zones. The random, inept fiddling with Photoshop sliders that passes for "photo analysis" among conspiracy theorists usually results in selective contrast expansion, amplifying what the JPEG engineers intended to remain very small and largely unnoticeable. And this is invariably attributed to some unspecified doctoring, simply because the faux-tographic analyst has no understanding of the underlying processes.
With JPG this is especially common near and around sharp edges of objects -- just like the edge of Neil Armstrong's bright white suit and the black sky behind him.
That's because JPEG engineers intended the process to apply to real-world photographs, in which there wasn't expected to be much high-frequency high-amplitude variance in any of the channels. The black background, in order to faithfully reproduce the space suit in the same zone, has to allow some dark gray pixels where the source pixels were uniformly black. If that zone is next to one of entirely black pixels, the contrast expansion will reveal a sharp boundary between the all-black zone and the black-and-dark-gray portions of the adjoining zone.
So what you are seeing here are nothing more than normal, expected JPG compression artifacts.
I'm always obliged to point out that JPEG, JFIF, and DCT are different things. JPEG is the family of compression and representation techniques. JFIF is the file format, what we call "a JPEG file." DCT is one of the many compression algorithms available to JPEG encoders. Not all JPEG compressions are lossy. However, so many people prefer the small file size that nearly every JPEG-encoded image is compressed using lossy DCT.
But the files would be huge, which is why the generally available versions of these pictures have all been JPG compressed.
To those of us who have worked with image compression, transmission, and analysis for something like 20 years, and have seen thousands of these artifacts (literally), people who say they're some kind of sinister plot to suppress the truth sound literally like someone saying cars are really monsters that eat children.