Purpose/Difficulties of having a common mode choke
A couple of months ago we had an in-house EMC basic training, and these are my two cents to the subject.

Noise

Line noise can be generated by the source itself, and/or due to electrical and/or magnetic coupling. Electrical coupling is mostly caused by capacitive coupling to traces which experience high dV/dt, while magnetic coupling is more preponderant in adjacent traces carrying high dI/dt. 

How common choke works:

There are already a couple of detailed answered questions available (e.g. What exactly happens to the signals hitting a common mode choke?) concerning this subject. Basically, the Common Mode Choke (CMC) has a low ohmic path for differential signal as the Magnetic Flux produce by each line cancels each other out, thus ideally no impedance is produced. As for common mode signals, their produced Magnetic Flux are in-phase, thus the impedance is increased.



Source

Now to your senior's comment:


  We found out that it (CMC) may be useful if there is no ground plane like in 2-layer designs but with 4-layer and greater, the ground impedance tends to be low enough that it won’t cause common mode problems


Analog Devices has a very interesting Article about how ground loops affect the PCB noise (see "Grounding for High-Frequency Operation"). 

Here is a small summary:
Consider a multi-layer PCB with a ground plane according to the following. The DC current returning from via 1 to via 2 through the GND plane will take the shortest path, as it has the lowest DC resistance. However, high frequency signals (e.g. noise) experience not only the DC resistance, but also the reactance due to the inductance of ground. 



This parasitic inductance is proportional to the loop area formed by the traces and ground plane as shown in the following image. Using the "right hand rule" you will find out that the current flowing towards the load and back to the source through the ground, generates an in-phase magnetic field inside the loop. 



Essentially, the larger the loop area is, bigger the parasitic inductance and high-frequency impedance are. However, the high frequency signal does not have to take this highly reactive path, it can ,and will take a path with the minimum reactance, meaning the one which forms the smallest possible loop, according to the following:



Assuming now that there is no ground plane (double-sided PCB for that matter), but only a ground trace, the noise would have no choice but flow through this highly reactive path. For high frequency signals (noise again), it would lead to an induced  voltage proportional to:

$$\Delta V = L_{gnd} \dfrac{dI}{dt}$$

Here you can see the effect of not having proper grounding of your PCB. As described above, the use of a CMC in this situation is beneficial as it reduces the ground loop by creating two magnetic fluxes which cancel each other.


  The other reason is that for the common mode choke to work properly, it becomes a tough job in layout, you need to guarantee that there is no overlap between AGND and digital ground on all layers ...


I reckon he meant, that if you have different grounds overlapping each other, the magnetic field of one ground will induce a (differential) current in the second ground. However, as the name says, a CMC attenuates only common mode noise, thus the noise picked up from the first ground will not be reduced.


  ... and you have to create a large puddle around the connector and you have to tie all the decoupling caps to that puddle with enough isolation otherwise noise will couple on the puddle and defeats the purpose for having a common mode choke. It’s not necessary to go through this pain and actually may hurt EMC if it’s not done right."


By puddle I suppose he meant "island" and the addition of capacitors is necessary in order to also reduce the ground loop by creating a short at high frequency according to the following. The surface of this "island" can increase the noise pickup, by capacitive coupling electric field from other parts of your circuit.