After Kissinger was brought up in debate, and seeing him mentioned so frequently on reddit now, I realize there's probably a lot of modern history that I don't know about very well for various reasons. What are some of the most egregious examples of this and what book(s) should I read to get outside this bubble?
"History of the 20th century" is...a lot. I have half of a book case on basically the 1910s and early 1920s. You will need to specify here, do you mean particularly American history? What aspects of it?
I can't recommend one book based on what you have posted. I would recommend you listen to people of all political views, though-Americans of all political stripes have a nasty habit of ignoring inconvenient historical facts. I got to go to school in both left wing and right wing districts, saw teachers of both kinds, and know that you can get an entirely different "history" based on chance.
I'd also mention that much of the Cold War is looked at through a primarily American-centric prism rather than through local politics influenced by the Cold War. If you read about Kissinger, you'll come across this frequently whether it's the Left or the Right, although for entirely different reasons. Part of the reason I occasionally worry about the knowledge of history for our generation is that they'll look at Google and accept whatever they see in the first page as gospel truth, without any deeper analysis.
For Kissinger specifically, what are you interested in? Operation Condor? Sino-Soviet politics? Vietnam?