I'm using an ATtiny24 (8MHz, internal RC oscillator, 5V) to control a LED driver, essentially an 8-bit shift register with internal current control. Total current is about 1.5A.
I've added decoupling capacitors close to the mcu. I started with 100nF and just a couple of µF and ended with several 1000 + an inductor to keep high frequency stuff away. The brown-out voltage is set to 2.7V. Sometimes adding 220µF causes the chip to do repetitive resets.
On my scope I can see some noise on the supply lines, but nothing that would dip down to anywhere near of 2.7V, the worst spike I could see was 500mV. According to the datasheet the BOR module kicks in after about 5µs below the limit, nothing about dV/dt activation (which could explain the bahaviour I see). I should add that my scope is pretty old and it's likely that I miss short glitches. Even worse in storage mode.
The only way to make it work properly is to disable the brown-out reset completely. After that it works just fine.
The same setup (LED driver + load) works with a different 'dev-board' (ATtiny4313 + active BOR @ 2.7V), which doesn't have any fancy supply line filtering either.
Broken BOR module or chi imbalance ?