A paper without any citations is generally considered such a bad source that it's only one step up from wikipedia. You can cite it, if you must, but you better not base your research on it. So in practice I don't think it's a big deal that mistakes aren't corrected and that academics typically aren't expected to publicly admit that they were wrong. It's just not necessary

Suppose the paper supposedly proves something that lots of people wish was true. Surely it is likely to get an immense number of citations.

For example,the paper supposedly proves that America always had strict gun control, or that the world is doomed unless government transfers trillions of dollars from group A to group B, by restricting the usage of evil substance X, where group A tends to have rather few academics, and group B tends to have rather a lot of academics.