If I roast a selection of mixed nuts, does it significantly change their nutritional content?
Also: Are there any potential food safety issues around roasting nuts (e.g. does it damage the oils)?
Discussion of the long-term health effects would be little more than speculation; however, there is a specific nutritional claim which can be tested, and has been tested in the commercial food-processing setting.
You'd have to read the whole study for a detailed analysis of how roasting affects the lipid oxidation products, which are the same products seen in rancid or overheated fats, but there is going to be some effect.
This is really more of an issue in a food plant because they use big machines designed to roast huge quantities of nuts (we're talking 200 kg/h for a low-end, $5000 gas-fired machine). The heat characteristics of one of these machines is going to be completely different from the comparatively slow roasting of a tiny quantity of nuts in a home oven, so don't panic.
To be any more specific, you'd have to specify the kind of nut. The oils from different nuts peroxidize at different temperatures; some unrefined nut oils start to smoke at around 160° C / 320° F (peanut/walnut), others go well into the 200° C / 400° F range (e.g. almonds). In any case, it's very rare that you'd actually be heating the nuts up to these temperatures unless you left them roasting too long, and they'd smell very burnt at that point.
Just don't eat hundreds of pounds of roasted nuts every month, and don't burn them when you roast them, and you'll be fine.
Here's a good article addressing your question:
Edit: To paraphrase the article... In a nutshell, yes and no... Roasting nuts over 170 degrees Fahrenheit (75 degrees Celsius) can damage the fats, causing the the fat to break down (and potentially release free radicals)...
The article advises against commercially roasted nuts because you don't know at what temp they were roasted
Roasting nuts under that temperature should maintain their nut integrity :)