How much does a Zobel network and its components affect the sound of speakers?

You definitely need the zoebel and might see an improvement in sound with new parts if the current cap and resistor are out of spec or defective.  
the zoebel is not a critical part of the crossover network that would lend itself to sound quality upgrades with improved quality parts.  
If you have DIY capabilities those parts should be inexpensive all things considered if you are determined to give it a try.  

Caddock MPs are 10W resistors.  Vishay/Texas Components Z-foil are .25W.  If you want to experiment, use 10W alternatives such as Path, Duelund, Mills, or ebayed Russian SSG silver mica.  

A few thoughts about the Merlin RC Networks (or Zobels).

Merlin made two types of RC’s. The “Standard RC” was made with the Hovland cap and the Caddock resistor. The “Master RC” was made with a custom spec Duelund VSF type cap and the same Caddock resistor. The caps used in both networks were the same value (0.01uF as mentioned above), but the Duelund cap costs about 10 times more than the Hovland cap (I know this because I have Duelund make me the exact same parts today as I make new Merlin Master RC networks, exactly as Merlin made them, for customers who want them today). While this makes the Master RC’s much more expensive than the Standard RCs  (which I also can make for folks), the Master RC’s do sound better.

The Merlin Zobel, interestingly, basically comes into play around 1.0Mhz (at 20KHz its impedance is around 800 ohms) and it is basically providing a way for RFI frequencies that appear at the speaker terminals to be dissipated.

IMO, since I find later/last version of Merlins made to have less coloration or noise due to improvements they have in the crossover caps, and internal wiring used - I think the effect/benefit of the Master RCs is more audible.

Duke is correct that the speakers (TSM and VSM models) have a quite flat on axis frequency response, though due to the characteristics of the soft dome tweeters Bobby used the on axis response in the treble is a little rougher on axis. The speakers were recommended/designed to be used as noted in their user manuals At around 10 to 15 degrees off axis as there is where the frequency response was the most smooth/flat. Yes, the speakers have fairly wide dispersion and some attention is generally needed if they are placed near reflective sidewalls for best mid-top frequency performance.  IMO/experience, often any edginess can be corrected with some basic room treatment or proper speaker placement (as discussed in the speaker manual). I do notice in the later models/version (i.e. “Black Magic” edition versions) of the speakers, that the speaker’s upper mid/treble performance is very clean/even/smooth. Clearly better than in older models. I don’t know if the speakers have the exact issue Duke refers to (it is possible), I think I have some off axis frequency response curves somewhere which would give a idea if that is the case or not.

Happy listening,
Rich

Rich, My MMIs are Serial numbers 4168, if that tells you anything. Your information is interesting, but it tells me nothing specific about how the RC networks and their particular components affect the sound, nor anything about how swapping components might do so.

@signaturesound That makes it sound like a worthwhile upgrade to any speaker. Could you also say what value the resistor is in the zobel circuit? I'd be interested in building a pair and trying on my coincidents.