Also have this issue with the base model M1 Mac Mini - have only ever used a single display at a time with it and have seen the small pink squares (horizontal line of them across the screen roughly in the middle) on 3 different monitors (two Dell U2412m and one Dell P2214h) and using either a HDMI to DVI cable or a USB-C to DisplayPort cable (the monitors have VGA, DVI, DisplayPort inputs). All of the monitors and the HDMI to DVI cable have been used with Windows computers for years with no issues whatsoever.
They look identical to the pink squares other people have posted and are on the desktop (I use automatic login) immediately after booting up from cold, the mouse cursor covers them rather than going behind them - they seem to go after a few minutes and/or if you fiddle with the wallpaper/colour profile etc in System Preferences. All options for Spaces (as suggested earlier in the thread) are unticked, though that is presumably only relevant to multiple displays anyway.
Seems like no other possible fixes yet? Anyone got a reference number or similar to mention if calling support so that they can link the calls together? (haven't tried calling yet)