> strange shapes and squares.
I bet they're all in nice neat 8x8 blocks.
That's how JPEG compression works. It divides the image into 8x8 blocks and then works out how much of various standard waveforms are needed to approximate the input image. When you turn down the Quality setting it allows the encoder to be sloppier. At low levels it's sloppy enough that the borders of the 8x8 regions become obvious.