As a Fellowship Group Spiritual Overseer you will serve the group by providing prayer and biblical guidance. You don't have any direct tasks to complete at your weekly Fellowship Meal, but you'll provide a foundation of support that helps the group stay on course with doctrine and application with your periodic input. You should pray regularly for your group members, have your “ear to the ground” at the Fellowship Meals (and in other contexts), and periodically verbalize some encouragements/course corrections to promote biblical understanding and practice.
The ideal person for this role is gifted in biblical knowledge and doctrine, and has a deep love for the Church.
This is one of your primary roles, and if you fail here, your other service to the group will be greatly weakened. Don't neglect this–prayer is time well spent!
We'd like to maintain a gracious understanding of doctrine by "majoring on the majors" and "minoring on the minors." When it comes to the doctrines of salvation, we must be rigid. With secondary or tertiary matters, we must not be too quick to speak, but instead gauge what's going on in the heart more than the "letter of the law." (In time, we will develop our own essential doctrines, but for now, stick with what is historically orthodox and what you find here.)
If a minor error is verbalized, no worries; We have people of all spiritual maturities and biblical knowledge in our church, and you don't have to be the "doctrine police." But listen for what is repeated over time, and if something consistently comes up that you don't find in alignment with Scripture, take note and pray for wisdom on when/if to address the matter. If, on the other hand, some more blatant heresy presents itself, we must have the boldness and care for the flock to address it. (If you're ever wondering what to take a hard-line on and what not to, please talk to the Jared and the other spiritual overseers in our church.)
Also, and just as importantly, listen for what is good that is talked about among the group! Rejoice as you hear people being sharpened in their understanding of what God calls us to!
3. Encourage/exhort/correct the group or individuals with Scripture
You may choose to do this in a group setting (e.g. the Fellowship Meal), or it may be better to pull an individual aside–use discernment–but at times you should feel the necessity to speak up! (More often than not this will come in a planned way, not necessarily "in the moment.")
This shouldn't always be in the form of correction, but also encouragement! For example, maybe you've noticed right belief and would like to encourage the group in their whole-hearted practice of what they believe. Remember: "The theology that matters is not the theology we profess but the theology we practice" (Chester and Timmis, Total Church). Help in not just steering the group away from false doctrine, but shepherding them toward what is true and good!