After enabling DEBUG I found out that the errors was not in my Woody Snippet code, but actually in a plugin called PHP-Code-Widget caused by the deprecated PHP function create_function(). After fixing that, I found out that this error was also in the Slider Revolution plugin. I have a feeling that I'm going to find this error in other plugins too.
I also noticed that this problem did not happen with every page that had a Woody Snippet shortcode so I'll investigate that. I have about 5 other WordPress problems which I believe might be associated with this deprecated PHP function.
I will spend some time over the next few days to try to diagnose what's actually happening.
Thanks for your help so far. If you have any suggestions please let me know, and if I can pinpoint the problem, I'll let you know.
Dave.