There are several places, at least for now known to me where the game can consistently crash. Not only you will lose progress if you didn't save, but the game will also forget all the cinematic saves that were unlocked during that session, whether you were saving the game or not.

• Attempting to call any menu while "Anachronox Intro" or "Fatima Stops Boots" begin.
• Loading the cinematic autosave "Going to Sender Station"
• Destroying the holograms during Rictus fight (Use as little AOE skills as possible)
• Using keyboard to order bivice (an elementor which allows to have 2 input bugs) mystech attack (when selecting the input bug)
• Loading a save made during a battle (crash if used after restarting the game, softlock(likely) if in the same session).
• The battle after "Lost in Space". It is very special, it is not happening on the "Chamber" map, it is a separate one, related to the cinematic. All characters here have maxed out hp for some reason and using mystech here, at least with keyboard led here to crash several times. So I'd advice to just wait for Rho's special(Plasma Wall).