I agree, it's tough to come up with anything stands alone as even halfway credible.
Most of it is persuasive only if you already hold a particular set of beliefs. For example, if you are a conservative Christian (I am not) showing that Podesta participates in (arguably) Satanic rituals is credible evidence that he more likely to abuse children. Is it "evidence" that his brother has risqué art depicting children on his walls? Yes, if you believe that only a pedophile would possess such art, or condone someone else's possession of such. I believe these conclusions are wrong, but are logical within a particular moral framework (that I don't share). So without knowing your beliefs, I may not be able to come up with anything that you view as credible.
For me, I find the NYT's portrayal of Alefantis as "just a pizza store owner" to be sufficiently disingenuous to be of note. Regular pizza store owners don't get listed as one of GQ's 50 Most Powerful People in DC. Alefantis was the romantic partner of David Brock (the founder of Correct the Record) and was a losing co-defendant with Brock in a lawsuit characterized as "blackmail". If you start with suspicions about someone, and then later find that someone has been successfully sued another party threatening to "spill the beans", I think this is weak but credible evidence that your suspicions may be justified.
There are leaked Stratfor emails where Pizza appears to be the name of one of their projects: https://wikileaks.org/gifiles/docs/13/1326067_testing-the-pi..., https://wikileaks.org/gifiles/docs/13/1319020_pushing-pizza-.... This lends credibility to the idea that "pizza" might be a code word in emails like this: https://wikileaks.org/clinton-emails/emailid/23757. Personally, I read this as testament to the quality of New Haven's apizza (http://www.eater.com/2014/3/18/6264277/the-definitive-guide-...) but I can see why someone not familiar with foodie culture would have trouble taking Clinton's response literally.
Last, I think that the discovery of prior accusations of Podesta's involvement in pedophilia is relevant. A year before his death, Andrew Breitbart tweeted that Podesta was a "world class underage sex slave op cover-upperer": https://twitter.com/AndrewBreitbart/status/33636278100561920. As an accusation without proof, it means very little, but if an independent path leads to the same conclusion, it becomes stronger. Still weak, still circumstantial, but if the discovery was truly independent, it seems like enough of a coincidence to justify looking closer.
But yeah, I find all the evidence to be weak and circumstantial. With a different set of beliefs/prejudices -- or if you have a strong intuition for the power of confirmation bias -- coincidence is the best explanation. But I think it's worth trying to understand why a subset of people genuinely do find the evidence to be credible, even if it's not.