Found three of them:
1) Using the shift-click to put a chainsaw from your hotbar into a chest while the chainsaw is active does NOT stop the chainsaw sound from playing. Is stopped when you bring the chainsaw back out and switch items again.
2) Dying while a chainsaw is active does NOT stop the chainsaw sound from playing in that location.
3) Chainsaws (and drills for that matter) do NOT play their respective "block-break" sounds - chainsaw grind, drill whirr...