The 1986 amnesty is still having a major impact, over two decades later. Teresa Watanabe of the Los Angeles Times offers "Settlement opens up amnesty for tens of thousands of immigrants" (link):

[The LAT's poster adult] arrived in the United States from his native Turkey with a valid student visa in 1981, but fell out of legal status when he failed to enroll in school, he said...

Thanks to a recent legal settlement, the chance to apply for amnesty is finally open to [the poster adult] and tens of thousands of others who entered the country on a valid visa but fell out of legal status between 1982 and 1988. The settlement, approved this fall by a U.S. district court in Washington state, stems from a class-action lawsuit filed by attorney Peter Schey originally on behalf of an immigrant assistance program of the Los Angeles County Federation of Labor, AFL CIO...

The landmark reform law offered a one-time amnesty to immigrants who were in the United States unlawfully from before 1982 to about 1988.

But Congress was concerned that those who entered the country with a valid visa would argue that they fell out of legal status during that time simply to qualify for amnesty. As a result, Schey said, Congress created a rule requiring immigrants to show that their shift from legal to illegal status was "known to the government."

That rule, however, created a new problem: How to prove that the government knew about their violations?

Every "problem" has a "solution", and any "problems" with any new amnesties (aka "comprehensive immigration reform") would have their own "solutions". For a reverse-Kafkaesque example, see this:

[Schey] also successfully argued that the government knew many immigrants had violated their status another way: by failing to furnish an address report every three months. The government's failure to produce the address reports showed that the immigrants had not filed them, violating the terms of their visa, he argued.

Note also that, as befits the LAT Style Guide, the fact that Schey has a series of links to the Mexican government was not in the article.