Something I've always meant to do in this forum was to start a thread about border crossings so that people could compare what happens. Why you may ask? Because when I crossed into Chile from Mendoza, I never paid a fine for having an outdated tourist stamp and they never entered info into a computer. The guy asked for the "paper" (a slip included from when I went to colonia) but I said I didn't have it. He just shook his head and rolled his eyes but let me through anyway. Coming back in at the crossing up there in the mountains was a rubber-stamp affair basically.
I've taken the ferry over to Colonia and come back and know that's strict regarding the visa and the security compared to other border crossings is much stronger. They also added a small exit/entry fee, which didn't happen at other crossings. Coming down from Bolivia into Arg, I was ushered into a tourist line so I didn't have to wait and had my stamp within seconds of walking up to the window. Immigration at the BA airport wasn't difficult but they are going to catch you with an outdated visa and NO, it doesn't help to get a new passport since all your border crossing come up on the computer screen. At least the ones at computerized crossings.
I crossed borders and came back to renew my Visa 2 times before deciding this isn't worth the hassle. For me, it came down to if I wanted to stay permanante or not. If you're serious about staying or want to own property, then get legal. If it's less than 5 years and you don't need the resident papers to survive (work, apt) then it's not that hard to hide away and fly under the radar.
And sorry if this sounds racial, but foreign people from wealthy countries DO get treated better than natives from local countries. Those are the ones that the immigration cops are looking to bust. And no offense to Argentina, but it's often easier to do things illegally than legally. They have a pretty easygoing attitude towards personal corruption, like it's normal or expected.