I am a physicist. I strongly disagree with your view that the methodology is sound.
The measurement methodology for the 'power out' was not the way I would do it. It effectively comes down to measuring the temperature of the 'reactor', in air, and applying calculations. Temperature is measured via an IR camera. It is filled with many ways that they could mislead themselves. I have personally used such a camera to measure surface temperatures in a high power density accelerator target and it is far from a straightforward enterprise. Why not just load the whole thing into a bomb calorimeter? That's the immediately obvious way to measure what they want to measure.
They do not adequately describe their power input. They start out with 3 phase. There's some kind of power supply box in the chain before the resistors. Who supplied this box? More details on what's actually measured as 'input power' is required. Is a circuit diagram too much to ask for?
The isotope data would be compelling. However, it's clear from the paper that Rossi handled the fuel at loading, removal and possibly at points in between. Substitution would have been trivial.
No radiation was observed. LENR, cold fusion, whatever you want to call it where no radiation is emitted is completely incompatible with all known nuclear physics. The idea that it doesn't violate any known physical laws is nonsense.