I'll go with jtbell and Dalespam on this one.
There are many different interpetations, of which the one alluded to by DaleSpam is probably the simplest. DaleSpam's approach is based on Feynman's ideas, which you can find outlined in "QED - a strange theory of light and matter".
The problem is that Feynman doesn't tell you how to calculate anything. Apparaently the path integral approach can be made to work, but unfortunately I don't know the details of how to get usable answers out of it - and while QED is otherwise a good book, having an "answer" that doesn't actually let you calculate anything turns out to be a lot less useful than one would hope.
But Feynman and QED will proide a nicely quantified example of a simple situation where assuming that a photon follows a single path does not agree with experiment. He will, in other words, give you some good questions. And the question of most interest are the famous single and double slit experiments.
First off, if you assume that light travels in a straight line, you can't account for the diffraction phenomenon that occurs when it passes through a single slit.
WHen you have two slits, things get even worse.
If you assume that the light travels in a straight line through one slit, or the other, and add the results together (perhaps throwing in diffraction on an ad-hoc basis), you will not get what is actually observed, which is the double-slit interference pattern.
The "simplest" explanation for the interference pattern is up for some debate, Feynman's explanation is basically that the light travels through both slits, and interferes with itself.
Since multiple posts aren't allowed, you might want to move your thread if you want better answers from the quantum people. But this is pretty much the basics.
The very short version is that diffraction and intereference can't be modeled in the way you suggest. If your in an experimental realm where neither effect is important, you might get away with it.
