The things that it takes to get a M4C lurker out of their hole… 
Both of my Saigas ran without issue out of the box. I bought my first years before the current spike in cost, at the time one could pick up either Saiga 12s or 20s for $250-380 per… I don’t know if I’d have bought one at current prices.
There were a number of early models that were quite unreliable, unaffectionately known as “vodka specials”, as a previous poster mentioned. No longer a problem with more current production.
The manufacturing tolerances are not extremely consistent, so functionality with any particular load may vary from gun to gun. Mine shot whatever I loaded in them. Others may have difficulty with some birdshot loads, such as with some of the cheap universal Walmart stuff, for example. It’s just necessary to find those that work well on your individual gun. Winchester AA’s are one of the better choices for light loads. Buckshot loads don’t seem to have the feeding issues that some report on the light stuff.
The gas piston may require cleaning for proper function anywhere from several hundred to several thousand rounds. That said, on my range Saiga I haven’t cleaned the piston in around 2,800 rounds, more out of curiosity than anything, and despite incredible amounts of fouling, I have yet to encounter any issues with it impacting function.
The only problems I’ve experienced have been with aftermarket box mags. AGP Gen 1s can have feeding issues. Both of mine required disassembly and sanding for proper function, and I keep them only for range use. AGP Gen 2s are good, though the factory Izhmash 5 and 8 round mags are built like tanks (metal internal reinforcement, Russian milspec polymer/springs, etc), and might be the best choice if one is willing to pay the cost. The Izhmash 8s will run you $120-$150 per mag, and are hard to find. Many report good experiences with the Surefire 10 and 12 rounders, though I can’t speak from experience. Some report deformation of shells left in 10 and 12 round mags for prolonged periods of time, inhibiting proper feeding, as well as tensile strength issues with the springs on some brands of 12 rounders left loaded, though I’ve had neither of these issues with 10 round AGP Gen 2s.
The mags are rock and lock like other Saigas and AKs. Loading full mags on a closed bolt has been a reported difficulty, though I didn’t have an issue with it. Could be mag design, or simply the inherent differences in tolerances from gun to gun. Some Saiga gunsmiths do a mod specifically to make loading on a closed bolt easier with 8 and 10 round magazines, though again, my Saigas didn’t have an issue with that even prior to the trip to Tromix.
As earlier posters noted, there are aftermarket gas regulators available to adjust your gas up or down depending on the needs of your individual gun. Functionality and recoil on any given load can change noticeably, depending on your gas setting.
Good mags are perhaps your biggest concern as far as reliability goes. As far as modifications, there are pros out there that are willing to do nearly anything you can think up to a Saiga, from basic reliability tweaks to truly crazy stuff. Tromix, R&R, Etac, Red Jacket, Cadiz… though the legal modifications are more limited in NJ. Take a look around the Saiga-12.com forums, and search the information that has been posted. There are a a few people there who know a lot.