If you hadn't noticed, more than a few people like his positions on foreign policy and the drug war. Those two issues are points of attraction for many on the left. We've gone over Paul enough for you to know that I'm not one of his fans. I think his primary appeal, across the political spectrum, is that he offers an alternative vision for the country, in much the same way as Ross Perot did in 1992 (his 1996 run didn't have the same spark). It's clear and compelling and wrong.
Granted, the newsletters are not specifically mentioned in the paragraph. Given that they are a constant presence on DU, I would hope you could forgive me for mentioning them.
There is only one issue that I think makes him attractive to the left, though it underlies multiple issues. That is civil liberties. He constantly speaks about a "loss of our freedoms" to the encroaching power of government. The attraction of this is no surprise. Consider it blowback from the Bush years. You can't expect people to spend most of a decade bemoaning the gradual encroachment of the national security state and then magically turn it off just because the president has a (D) next to his name. Rather than waste time trying to prove he's a liar, it would be better to show how his vision of government will simply give undemocratic groups the power to attack civil liberties. It's possible to reproach government for its failings and realize that simply removing government from the equation is counterproductive, at best. Attack the idea, not the man. The man is old and won't be around forever. The idea can keep floating out there for whichever idiot picks it up next.