Common-mode input voltage range (CMIVR) is the range of input voltages, which can be applied without that the chip produces an error. An error here means for instance that an output phase reversal occurs, or that internal circuitry hangs in a long lasting metastate, or what so ever. The manufacturer does not state in datasheet, what exactly happens when the CMIVR is exceeded. Nevertheless we should never violate CMIVR.

This functional input voltage range has nothing to do with maximum ratings, where the chip becomes damaged, by the way.

CMIVR of LM311 is about 0.2V...3.8V (typically) at Vcc=5V. So, without the zener (here a red Led) potential at inverting input can easily exceed CMIVR, if you have a look at the circuit:



With the 1N6263 at inverting input and Vcc=5V, input voltage can rise up to 5.5V.
Now you might tell, that transformer does not produce such a big voltage at output. But, as mains is extremely contaminated by noise, glitches, spikes, bursts and surges, you can not at all expect an anyhow limited secondary output voltage. For this you need the zener at input of circuit.

Kai