Anyone know why when I 'Print', it doesn't show on system notes, but when I print a 'picking ticket' it does? I'm hoping to find a way to run a report to see if items were printed or not, Some orders we print sales orders and others we print picking tickets.

the picking ticket shows because there is specific functionality driven from there. For your requirement to know if the SO has been printed, I would create a custom field and use a workflow display a button that will mark the custom field and true AND print the sales order. Users would need to use the custom button and not the native print icon.