How can I automatically classify peaks of signals measured at different positions?
It looks like you have a single source, x[n], and multiple microphone signals $y_{i}[n]$. Assuming that your propagation path from the source to the microphones is reasonably linear and time invariant, you and simply model the path as a transfer function. So basically you have 
$$ y_{i}[n] = h_{i}[n]\ast x[n] $$
where $h_{i}[n]$ is the impulse response of the transfer function from the source to microphone "i". These transfer functions have different amplitude and phase responses. If they are different enough, the individual microphone signals will be quite different as well and there is no reason to believe that the peaks will actually show up at the same spot. In most acoustic environments, they will be "different" if the microphones are more than a quarter wavelength apart for the frequencies of interest (or where there is non-trivial energy in the spectrum).

If you can measure the transfer functions, you can filter each mic signal with the inverse of that transfer function. This should make the mic signals much more similar and reduce the effect of the filtering. 

An alternative would be to combine all mic signals into a beamformer that optimizes pickup from the source but rejects everything else. This should also provide a fairly "clean" version of the source signal.