How do I troubleshoot Siri?
There isn't a lot you can do about holding it up to your wife's head, perhaps it isn't close enough. You will notice that if you try to fool the phone by holding it up to your had or arm siri will not activate. 

As for the geofenced reminders, you need to have location services turned on for reminders.

You will also need to set the address in your contacts, so add your home and work address to your contact.

For troubleshooting you will really need to look into the apps you are trying to control from Siri, as Siri itself is not an app, it is part of iOS. It is each individual app that will need to be looked at when troubleshooting.

Remember that Siri is still in beta and you can expect some teething problems with it.