Andrew Gelman just wrote a blog post regarding interaction terms in multiple regression and concludes:
You never have to do an F test. Just forget about that stuff!
I find it incredibly refreshing when someone (a professor, no less!) is willing to cut through the math and get down to common sense. And I particularly hate F-tests in regressions, since they are so frequently unhelpful. Yes, I get it - with many variables you increase the probability of a type I error and the F-test overcomes that. But I have yet to come across a vetted, sensible and non-hypothetical model in which F-test failed to reject the null but at least one of the marginal t-tests did. I know, never say never, etc.
Of course, I realize as I write this that you do have to follow quite a bit of math in this case, so we're not really cutting through the math as much as "intelligently disregarding it", but that's why we're nerds, isn't it?