Well, from what I know about the Anthony Weiner documentary, it's more a reality-show style type of storytelling. I was thinking more of feature films, but in this case, there's enough "infotainment" in these two picks by G-man that maybe they offer a unique perspective beyond more conventional documentary film-making.
I haven't heard of ANY of the picks in you guys' last two posts, stuff to explore.
Two more to add to the list (a film that covers some of the same behind-the-scenes as the Weiner documentary that G-man listed) is
The Candidate (1972) starring Robert Redford. Where Peter Boyle is a professional campaign strategist who moves from one campaign to the next. His next project is running against a Republican Senator who is considered unbeatable, and just to fill his time, he approaches a young activist lawyer (Robert Redford) to campaign, with the assurance Redford's character can't possibly win and won't have to actually hold office. It gives behind-the-scenes about shaping political image in stump speeches, political TV ads, fielding attacks and gaffs, televised debates and other aspects of running a campaign.
The scene at the end where Redford says to Boyle: "This wasn't supposed to happen, what do we do now?" is a scene that went through my mind on election night in 1992 when Bill Clinton won!
Another great one by Redford was
All The President's Men (1977) that mostly factually portrays Washington Post reporters Bob Woodward (Robert Redford) and Carl Bernstein (Dustin Hoffman) over a roughly 2-year period breaking the story of the Watergate break-in of the 1972 Democratic National Headquarters, and "following the money" from the five burglars to the Nixon campaign officials, and into the Nixon White House staff.
The movie ran a few weeks ago again on TCM, and the commentary after said that Redford was friends with Carl Bernstein, and encouraged Bernstein and Woodward to write a book of their story, because it would be easier to option it into a movie if there were a book. So Redford was the catalyst that made them write their Pulitzer-winning book, that later became a movie!
Redford is a quintessential example of a Hollywood actor who has used his celebrity to have a profound influence on politics.