Updating directly from SP1 to SP3
You shouldn't have any issues, just be sure that when you plan your maintenance for SQL Server you don't get blocked by the "Restart Computer" rule. E.g. if you have installed Windows Updates in the meantime you might not know that Windows needs to be restarted until you enter your maintenance window...

For some background, I got surprised by this during a SQL 2012 Service Pack + Cumulative Update series recently. It turned out that I fired up the computer, started the Service Pack install, but didn't know that Windows Update had started performing updates in the background. By the time I got to the CU, the reboot flag had been set, and I was very frustrated since it seemed to me like the SP install had forced a restart requirement.

http://www.sqlperformance.com/2012/12/system-configuration/sql-2012-slipstream