Error updating sql server geography type in trigger
Try this one. I have moved the conditional update into a single statement because the action you were taking was the same for both conditions. Also I have altered the way that you join to the INSERTED table so that it performs the filter pre-join:

CREATE TRIGGER dbo.triggerGeocodedAddressUpdate ON dbo.Party AFTER UPDATE AS
IF UPDATE(Latitude) OR UPDATE(Longitude)
    UPDATE pt
    SET pt.GeocodedAddress = geography::Point(i.Latitude, i.Longitude, 4326)
    FROM dbo.Party AS pt 
    JOIN 
    (
        SELECT PartyId, Latitude, Longitude
        FROM inserted
        WHERE (Latitude IS NOT NULL AND Longitude IS NOT NULL)
    ) AS i ON i.PartyId = pt.PartyId;
    RETURN
GO


I hope this helps you.