What are the important questions about global warming?

I am writing a book for lay people on global warming. I want to look at it from the angle: what are the best, simplest, convincing arguments? The other main question is, what are the questions people trying to make up their minds are going to ask in order to be sure?

The one fact that convinced me was that there is no heating signature in the troposphere, whereas all GCMs say there must be. That's a killer, and I'll shortly write a blog about it. But what convinced you? And when you were investigating, what were the big questions on your mind?

This post is simply to provide an anchor for anyone to weigh in on these issues. In fact, if you were convinced that anthropogenic global warming is happening, what key facts convinced you of that? (Who knows, you might convince me to change my mind - it's always open. But don't tell me about 600 scientists or the IPCC or a consensus or the debate is over; tell me actual checkable facts.)

Over to you all!