What I took away from the article is this: whenever you're thinking of rewriting from scratch, there's a better way - incrementally replacing the code. It's not as fun, and it feels worse, but it ends up with much better code. I'm pretty sure this is nearly always true.
Joel outlines the reasons, but the most important one, imo, is this: you're not going to do a better job. You think you are, because you see that the code is a mess and think you're better than the people who designed it. And you're probably right (or at least, you know more.) But a system that has years of work on it is not something you can whip up again from scratch - you're going to miss all the same things they missed the first time, when they were designing it, and either recreate all the bugs, or make your new system a mess.
Incremental improving is nearly always the saner solution.