No real Achilles heal, except for maybe getting the carrier tabbed. All my rifles have tabbed carriers, although one of them I've been shooting with an untabbed one to see if and when the Gremlin would appear. No problems after 550 rounds.
As far as spare parts, the top of the list would be gas piston, gas piston spring, striker spring, and recoil spring. Then would come striker and firing pin. Then extractor, extractor spring, extractor plunger. Lastly, another complete dustcover, as those are more pliable and can be damaged relatively easily if reassembled hastily; you can put your extra springs on there and have it ready.
The best place I've found for springs are on Ebay, particularly this vendor. Two complete and new sets of springs for $20 shipped is a killer deal:
http://www.ebay.com/itm/Set-of-new-springs-for-CZ-858-tactical-vz-58-/121484685203?pt=LH_DefaultDomain_0&hash=item1c490d2f93
As for the rest, you might want to consider all the small parts like pins, plungers, etc. I found the vendors below to be the best. Numrich has Facebook shipping coupons every Wednesday, and if you call their order number during business hours there is a recorded coupon to use online. Bonesteel has good prices but shipping can take awhile. Ohio Ordnance has some of the best prices and will ship USPS if you call them. Will all the vendors, it's best to get a bunch of stuff all at once to save on the shipping:
http://www.ohioordnanceworks.com/parts/vz-58-parts
http://www.gunpartscorp.com/Manufacturers/CZ-33195/MachinesGuns-35901/VZ58SMG-38704.htm
http://www.bonesteelarms.com/VZ-58_c2.htm
(cont'd below)