To anwer the questions posed:
The original rectifier is less efficient than modern replacement bridge rectifiers, so should result in a stronger charge to the battery, when required. In a marginal system, this is a good thing.
The zener diode is a crude method of disposing of additional voltage. When I connect a smart battery charger to my bike, with the zener diode in the system, the battery never reaches a full charge. Conclusion: the zener is dumping voltage prematurely. In a marginal system, not a good thing.
Having said that, I still run the original items in my bikes and watch the battery voltage like a hawk, especially when riding at night.
Additional details on the "weaknesses" of the original rectifer and zener pasted below.
If charging is a problem for you, you may want to replace your probably-dried-out selenium rectifier with a Radio Shack replacement. Bridge rectifiers being a common element in electronics, RS supplies a 10 and 20 Amp replacement in modern solid-state silicon version for less than a 10 dollar bill. Be sure to mount it so that it can bleed the heat it produces into an aluminum plate which you cleverly build as a mount. The earlier RS bridges had spade connections, but the later ones seem to be straight wires, so you'll have to solder the wires on. The terminals are marked + for the one you'll ground, - for the one you'll connect to the battery -, and the ones marked AC may be connected either way to the output from the alternator. Also, be sure to "heat sink" the heat from the soldering iron by using your third hand to clamp a pair of needle nose pliers to the component side of the soldering site. Once you're done, you'll likely find that this little improvement makes quite a difference.
If your system voltage is still low after all this, you may want to try disconnecting your Zener diode. The purpose of this baby is .... wait for it ....... to _dispose_ of excess voltage, so that your charging system won't overcharge your battery, burn out your lights, etc. Although hilariously funny to those who find themselves without the juice to get home on dark nights, this is actually a truth for some. I've had batteries boil with the Zener disconnected, even with the lights full on, so be sure to check your charging voltage after you've replaced the diode, and find out if you need to disconnect the Zener. Theoretically, it shouldn't draw any current at all below it's "knee voltage" of 13.8 or so. The more savvy may want to put an ammeter in the circuit to the Zener, and see if there's any current draw below this voltage.