My Wii is old, could its firmware be the issue, or does a system update resolve Error 51330?

It's less likely that the Wii's firmware itself is the direct cause of Error 51330, as it's primarily a network configuration issue. However, ensuring your Wii console has the latest system update (if it can connect to the internet at all) is always a good practice, as updates can include network compatibility improvements. If you cannot connect to update, you might need to resolve the 51330 error first using other methods or perform an offline update if available and necessary.