Oliver's 14-minute segment isn't huge on jokes, and it hits many of the points you'd expect it to. There's video of the ill-advised comments from some Voter ID supporters that it helps Republicans. There's the emphasis that many people without ID are minorities and older people. There's the overwhelming lack of evidence of the brand of fraud that Voter ID laws are aimed at preventing. There's the fact that getting a simple ID card can, in some cases, not be very simple.
Where the segment goes wrong, to my mind, is near the end. Oliver spends a few minutes pointing out that lawmakers who push for Voter ID laws have been caught on camera "ghost voting" in their state legislatures. This is the practice for voting for another member of the legislature in his or her absence.
The implication is that lawmakers who are so concerned about people fraudulently casting votes in other people's names are doing it themselves. Hypocrisy! Oliver gets very excited about this point.
Maybe "ghost voting" is a bad thing. And Oliver probably felt the need to hit some lesser-probed aspects of this debate, given much of what he talked about has been reported on extensively already. But as an argument against Voter ID, "ghost voting" probably isn't the ticket.