I recently flipped through the "Cartoon Guide to Physics", expecting an easy-to-understand rehash of ideas I was long familiar with; and that's what I got - right up to the last few pages, where I was presented with a fairly fundamental concept that's been absent from the popular science media I've enjoyed over the years. (Specifically, that the uncertainty principle, when expressed as linking energy and time, explains what electromagnetic fields actually /are/, as the propensity for virtual photons of various strengths to happen.) I find myself happy to try to integrate this new understanding - and at least mildly disturbed that I'd been missing it for so long, and with an increased curiosity about how I might find any other such gaps in my understanding of how the universe works.
So: what's the biggest, or most surprising, or most interesting concept /you/ have learned of, after you'd already gotten a handle on the basics?
You, an astronomer, should always ask yourself: Giving this light pattern in time, what is the most probable source which would give me this pattern. Be it static or dynamic, whichever fits the best.
The standard approach is to simulate multiple possible sources and use Bayesian techniques, such as maximum likelihood, to evaluate which ones match the data best and whether the best is a good enough fit. The waveforms matching in LIGO is one of the extremes, given how weak the potential signal is.