The paper argues that, because it is possible to doubt whether you are doubting, and to doubt whether you are doubting you are doubting, and so on and so forth, that this is an infinite regress, and because infinite regresses are ugly and inconvenient, we should just throw out the whole chain and declare ourselves sure of the world.

Frankly, this is a bad argument. The author mentions you can solve the regress by simply denying that you can even know your own mental states, but dismisses this on the grounds it doesn't help reach the desired conclusion. (!!!) The author also goes to the trouble of claiming that some infinite regressions are 'psychologically stable' while others are not; no real argument is provided as to why it matters whether a regress is such or not, except that the author wants to get rid of inconvenient ones but not convenient ones.

The way to attack Cartesian skepticism is on its grounds and assumptions, not to accept the premises. Descarte was right, if you assume his priors. There are many people who do this, but the most systematic and determined one is probably Heidegger. I suppose that people who want to believe in 'pure reason' are not especially likely to go down that route, though.