When I complile a document to PDF, the italics get switched to underlined text.
I selected all of the text in question, then went to Format > Formatting > Preserve Formatting
Everything else works fine, including multiple sizes of text, bolding, underlined text, multiple headline sizes, bullet points etc.
Is this a bug? Or something I can fix on my own?
Thank-you! 8)
In compile’s Transformation options, deselect the option to convert italics to underline. So long as your output font has an italics variant, that will fix it for you. 
Thank-you so much! I have no idea how that box got checked in the first place, but am glad it’s fixed now! You’re awesome 
Is there a way of permanently unchecking that box for all of my current and future scrivener projects without having to manually do it for each one?
It depends on the preset you’re using. The “Standard Manuscript Format” has it selected by default, along with the options to convert smart quotes to straight and ellipses to triple periods (among other settings, of course). If you choose instead to format as “Original”, the compiler will add very little to your text as it appears in the editor–mainly just inserting empty lines between the documents. All your formatting will be left exactly as in the editor, and you won’t compile anything but that text–no extra “Chapter” title prefixes or that sort of thing.
Ok, well I’m going to experiment with that then. Thank-you so much! 
Alternatively, open the standard manuscript format, switch off the conversions you don’t want and then save it as your own preset.

Mr X