What does it mean to love the Lord with all your mind?

There are several components to intellectual love for God.

1. Dedicating our minds to knowing him.
2. Thinking clearly and truly about him so that we don't have false ideas in our minds.
3. Not being satisfied with merely an intellectual awareness of his attributes, character, and acts but intentionally devoting that mental effort to serve the affections (emotions) for God.

If a person doesn't move from intellectual awareness of God and right thinking about God to an emotional embrace of God, he hasn't loved God with his mind. The mind has not yet loved until it hands off its thoughts to the emotions where they're embraced. And then the mind and the heart are working in what feels like such harmony, and you experience it as both intellectual and affectional love for God.

I would much rather have people deal with media that have violence and sex in them where God is an urgent reality—though there are almost nothing like this in existence—rather than have media that is squeaky clean of everything bad but is also absolutely God-less.

I think TV and movies and most of the media hurts us 1) by its ignorance and apathy towards God and 2) by its triviality. So it's not only leaving out the one reality for which we're created, namely God; it's also constantly shrinking our souls down to the most silly kinds of thinking, so that the capacity for knowing God is being reduced. He's not just taken out of the picture; the capacity to appreciate something great like God is being shrunk down because of the absolute silliness of most of the entertainment people give themselves to.