The War Within features a wide variety of new special effect gear, commonly called cantrip items, and trinkets from the eight launch dungeons and upcoming raid tier, all of which are available for testing right now on Beta servers!
Although there are a great number of trinkets available from the eight new dungeons coming in The War Within, there are only two special effect weapons, one a two-handed agility staff and the other a two-handed damage dealing intelligence staff.
Keep in mind that the Season 1 dungeon rotation does not include the Cinderbrew Meadery, Darkflame Cleft, The Rookery, or Priority of Sacred Flame, so item from those dungeons will not be available at maximum level through Mythic+.
There are several special effect items in Nerub'ar Palace, including a special two-piece fist weapon and trinket set, a defensively oriented cloak, a necklace that restores mana to healers, and a magic absorption shield. Additionally, there are about as many trinkets as might be expected from a new raid tier, covering all roles and primary stats.