After some more searching I found that the screen artifacts start after this message (from dmesg):
[drm:gen8_irq_handler [i915]] *ERROR* CPU pipe A FIFO underrun
- Bug#884116: linux-image-4.9.0-4-amd64: screen atrifact... root
- Bug#884116: Further information sogerc1 .
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Hannes Eberhardt
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Agafnd
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Richard James Salts
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Jerome
- Bug#884116: linux-image-4.9.0-4-amd64: Similar ar... Warlock
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Jerome
- Bug#884116: linux-image-4.9.0-3-amd64: screen art... Mathias Bavay
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... agafnd
- Bug#884116: linux-image-4.9.0-4-amd64: screen atr... Sylvain
- Bug#884116: linux-image-4.9.0-3-amd64: screen art... Mathias Bavay
