Frostfire Bolt
It is affected by almost every ability that affects fire spells or frost spells.
The only exceptions are range talents which do not apply. Its range is fixed at 40 yards.
The Fireball/Frostbolt cast time talents do not affect it either, which is expected.
The direct damage part scales as expected with 85.7%. The DoT ticks 3 times every 3s for 9s total.
Permafrost affects the length of the Frostfire Bolt debuff. If you spec at least 2/3 Permafrost, you will get a 4th tick of the DoT.
The DoT does not scale with spell power any more and is pretty useless, it used to scale for some time during beta.
The whole spell always deals Frostfire damage all the time.
If Frostfire Bolt gets counterspelled, it locks out both, Fire and Frost spells.
Also, locking out either school will also lock out Frostfire Bolt.
When dealing with mobs that are resistant/vulnerable/immune to either Frost of Fire, damage calculation is based on the weakest type to inflict the highest damage.
Note that Ignite itself still does only Fire damage, so Fire immune mobs won't take any Ignite damage.
Frostfire Bolt threat is affected by Burning Soul and Frost Channeling, but they don't stack.
So you get 10% threat reduction if you have one of them or both. DoT and direct damage threat is affected.
Ignite threat however is only affected by Burning Soul.
Note that threat over time is mostly irrelevant in most raids right now. Burst threat on the pull can be dealt with by using Mirror Image.
This spell does not have very strong basic scaling, but it can compensate through its extremely powerful scaling by combining critical strike damage talents and Ignite.
It used to benefit twice from many talents because it dealt frost and fire damage. Most of the issues have been fixed though.