If ADHD is caused by brain structure, why isn't analysis of brain structure used to diagnose it? My understanding is that people with ADHD have different brain structure to people without. 

If this is the case, why isn't the difference of brain structure used to diagnose ADHD, rather than a series of questions relating to behavioral symptoms?
ADHD is not 'caused' by a brain structure. However, there are observable differences in the brains of ADHD sufferers compared to non-ADHD sufferers.

For example, ADHD sufferers have a disproportionately greater decrease in volume in the left side of the prefrontal cortex, as well as the posterior parietal cortex.

In addition, there is typically a reduction in the number of dopamine receptors, as well as a sensitivity to neurotransmitter activity. Thus, stimulants and cognitive enhancements are often used to treat ADHD.

This paper does a good, in-depth job of mapping networks and brain connectivity to ADHD. If you were to read it, you might notice a problem -- it isn't the case that there is one 'brain structure' that ADHD sufferers have that non-sufferers do not have, nor is it just one brain structure that is affected. The way that ADHD seems to 'work' in the brain is very complex, and there is still much to be learned about the brain before we can go about diagnosing people based on MRI data.

Furthermore, the line between ADHD and other mental disorders is not clearly drawn. Inattentiveness could stem from depression, trauma, or insomnia, for example. Mania and/or hyperactivity could stem from bipolar disorder or histrionic personality disorder. We are so far from figuring the brain out that we can only rely on context at this point in time.