Here are a load of queries that you could make.

Brand title searches limited by Publisher and Location

This query could be used in a country-specific TV search:
http://atlasapi.org/2.0/brands.json?title=east&availableCountries=uk&publisher=bbc.co.uk

Genre query

Genre query, limited by broadcaster for classic VoD style listings:
http://atlasapi.org/2.0/items.json?genre=http://ref.atlasapi.org/genres/atlas/factual&publisher=bbc.co.uk

Given a URI, find a specific format

Find, say, an embeddable version of a particular piece of content:
http://atlasapi.org/2.0/items.json?uri=http://www.youtube.com/watch?v=n_0N6tC4iWo&transportType=link

Content mentioned on Twitter

Mentioned on Twitter, but restricted to a genre:
http://atlasapi.org/2.0/items.json?playlist.uri=http://ref.atlasapi.org/hotness/twitter&genre=http://ref.atlasapi.org/genres/atlas/factual

Get stuff mentioned on Twitter that is embeddable

Embeddable content mentioned on Twitter, to make a playable set of videos:
http://atlasapi.org/2.0/items.json?playlist.uri=http://ref.atlasapi.org/hotness/twitter&transportType=embed

What’s on the BBC right now

The transmissionTime parameter will take milliseconds since the epoch, but you can also use ‘now’ as a shorthand function:
http://atlasapi.org/2.0/items.json?transmissionTime=now&publisher=bbc.co.uk

What TV shows are on BBC One

This uses the URI for the BBC One channel:
http://atlasapi.org/2.0/brands.json?broadcastOn=http://www.bbc.co.uk/services/bbcone/london&limit=2

Get details from an embeddable URI

If you have the location of a piece of media, get the information for the canonical Item:
http://atlasapi.org/2.0/items.json?uri=http://www.bbc.co.uk/iplayer/episode/b00s9cdt