As bmike mentioned, there are multiple places to enter an AppleID to be used with the various Apple services. Some apps use the main iCloud account where others can be configured to a different ID.
If the iPod is primarily for your son, or anyone else, I would recommend setting up the iDevice under his Apple ID then log into the family account for other services. I do this for my family and with a few minor issues, it works out very well.
In the Settings, scroll down to the iCloud option. That is the primary account for the device. Configure it to your son's account. (I use the naming scheme of iPerson, like iJason, so when I configure other accounts, I know this one is the iCloud entry) Enable the apps that will be unique to him (ie Contacts, Reminders, etc). However, turn off "Find my iPhone" here as we will enable it later.
FYI: All apps will use this account by default, including saving app preferences via the Documents and Data setting. This will allow each family member to play the same game but each have their own saved preferences (if the app uses iCloud for preferences). If all the devices were set up under Dad's ID, the preferences could be changed by the wrong family member.
Now go back to the main Settings and just below the iCloud option is "Mail, Contacts, Calendars". Select this and add a new iCloud account entering your family account info. (I use the nickname of iFamily). In here, enable the apps that will be common between all family members. For example, I use Contacts, Reminders, and Find My iPhone for all family members. Configuring all your devices to use the same account for Find My iPhone allows you to log into the icloud.com site and see all the devices at once.
You can now go back to the main Settings screen and set up the Apple ID for other services to use the iFamily account or each iUser account.
- Messages: iUser
- FaceTime: iUser
- iTunes & App Stores: iFamily so that any purchase is available to all devices but I recommend you turn off the Automatic Downloads or everyone will get the new item pushed whenever someone else makes a purchase.
- Music: Home Sharing - iFamily
- Videos: Home Sharing - iFamily
- Photos & Camera: iUser but turn on Shared Photo Streams and set up a shared folder for the iFamily account (done in the Photos app).
Game Center doesn't (yet) have a Settings entry so you will need to set the Apple ID from within the Game Center app. Click on the Me tab and scroll down to the Account banner. If it isn't set to the primary iCloud account already, click the banner and log out/log in to the proper account.
Not exactly related to Apple ID but still a per user setting is the Twitter and Facebook settings. You will probably want to set these to the primary device user if they use these services.
I hope this helps. While looking up some details to post, I came across this Gigaom.com article which has a nice table laying out each app setting.