High speed PWM sometimes glitches out my gate driver
There is no common mode filter on the output. 

Thus, the whole Peltier assembly and its wires are at an ill-defined HF common mode potential, but it sure includes the nasty fast PWM edges which will go through the inductors' interwinding capacitance unimpeded.

Besides wrecking communication with the arduino (not surprising) this should be a rather powerful radio jammer.

Solution: put caps between both outputs and ground, instead of just between both outputs. 

A common mode choke would have been nice too. The best would be CM choke, then two small caps to GND after the choke.

EDIT

I had missed the fact that the "ground plane" at the back is full of traces, and the arduino connector is located in a very noisy position. This will be harder to fix... maybe thread the arduino cable through a ferrite core?...