Had to say without looking at your sript. What actions are NOT allowed for your non-admin user?
You may find it very helpful to run your script with the debugger enabled. (You can doe this even when the file is open with the limited access password) and watch to see exactly what step trips this error.
There is a selection on the script editor window to run with full access privileges. You could check the box and it should allow the script to run.
However as Phil says knowing exactly what step is making this happen would be preferable. It could be as simple as temporary layout navigation that the user doesnt have access to but the script should. Without the detail we wont know.
Thanks both, I opened the Script Debugger and selected a value from the Pop-up list but the error occurred before the script loaded. Also tried the Full Access Privileges checkbox but that obviously doesn't come into play as the error appears to be occuring before the script starts.
I'll investigate Record, Layout and Value List privileges next...
Found it, the Global field for the Pop-up list was set to "view only" in the 'Custom Field Privileges'. Changed it to "modifiable" and it works great for the User, many thanks...