Amazo -the android that has the ability to duplicate the powers of metahumans. Certainly not a walk in the park for our heroes.
Dr. Destiny - A evil scientist that created a device which allowed him to create reality from the fabric of dreams. Not a threat? I suggest reading "Justice League: A Midsummer's Nightmare."
Despero - alien from the planet Kalanor, and in addition to a genius intellect possesses a third eye on his forehead capable of hypnotism, illusions, telekinesis and telepathy. He originally appeared average build, but now appears to be of a physical threat as well.
Prometheus - or as I call him "the Anti-Batman." A son of criminals who were shot dead by police in front of him, he made a vow to "annihilate the forces of justice." He uses an extensive range of equipment and technology as well as being tough mentally and physically. Common tools include body armor; gauntlets that fire various projectiles, and a helmet that download the knowledge and physical skills of others directly into his brain.
Eclipso-The incarnation of the Wrath of God and the Angel of Vengeance who turned evil and was replaced by the Spectre. Eclipso's ability to possess one who touches the cursed diamonds makes him a big threat. Imagine the League battling a possessed Superman on the big screen. :)
The Hyperclan/White Martians - The Hyperclan were white Martians who came to Earth to displace the affections of the planet from the League to them. Like the Green Martians, White Martians have numerous superhuman powers - strength, flight, invisibility, telepathy, shape-changing, and phase-shifting, but they also share the Green Martians' vulnerability to fire.