In my (funny) opinion: A circuit without a capacitor is no circuit ;-)
So in case you encounter any instabilites, then maybe you just need to decouple the power supply and the DC levels.
Maybe even the measurement signal path with a suitable C.
All Cs should be referenced to the same common GND point. Or better use a solid GND plane. (No copper pour)
From what I understand, hysteresis is a method to make one comparator act like two as in your window comparator.
When the input volt level causes a change of state, afterward the input must meet a different new volt level in order to again change state.
The two trigger levels are automatically determined by the proportion of positive feedback tapped from the voltage at the output.
It's not necessarily easy to adjust hysteresis so that you obtain a desired range of operation with one device.
Sometimes it's easier to build a window comparator using two devices, and set trigger levels wherever you wish.
Yes, because the schematic is incomplete. It doesn't show how the IC's hysteresis feature is set up.
The datasheet shows window comparator schematics. Also they use the IC_internal REF, which usually is more accurate, precise and more low noise than a supply voltage. I recommend to use the REF, unless the application really needs to refer to the VCC level.
According to my understanding of the datasheet, LTC1841 has no built-in hysteresis. The datasheet is somewhat confusing in this regard, the title lines give the impression that the features apply to all LTC184x types, but they don't. You can however simply add a posistive feedback resistor to the schematic appended in post #1.