Be careful when using this ability if you're fighting ranged-weapon-using mobs, since you could end up intercepting a ranged attack towards a party member which is actually far from all mobs, and doing so you'll not only end up far from them as well, but also pull the melee ones near him.
On some bosses if performing as an offtank, when your job has ended you can help with the survival of the main tank by using intervene when he has very low health. You take one boss melee swing yourself, giving healers a bit more time to heal main tank up. Be careful when using this though, because Intervene also reduces the threat of the target you use it on, so don't try it on threat sensitive fights.
Also, similar to the above, you can use Intervene's threat reduction specifically for that. Intervene a DPS close to the MT in threat for a small reduction in hate, allowing them to continue DPSing.