Quicken Spell (Metamagic)
You can cast spells in a fraction of the normal time.
Benefit: Casting a quickened spell is a swift action. You can perform another action, even casting another spell, in the same round as you cast a quickened spell. A spell whose casting time is more than 1 full-round action cannot be quickened.
A quickened spell uses up a spell slot four levels higher than the spell's actual level. Casting a quickened spell doesn't provoke an attack of opportunity.
Special: You can apply the effects of this feat to a spell cast spontaneously, so long as it has a casting time that is not more than 1 full-round action, without increasing the spell's casting time.
Spell Critical (Su): At 10th level, whenever an eldritch knight successfully confirms a critical hit, he can cast a spell as a swift action. The spell must include the target of the attack as one of its targets or in its area of effect. Casting this spell does not provoke an attack of opportunity. The caster must still meet all of the spell's components and must roll for arcane spell failure if necessary.
The text of these two abilities basically changes the casting time of a spell to a swift action and makes them not provoke. Otherwise nothing else changes.
You still need a free hand to cast a spell with somatic components.Somatic (S): A somatic component is a measured and precise movement of the hand. You must have at least one hand free to provide a somatic component.
Also, casting incurs the normal spell failure.
Spell Failure
If you ever try to cast a spell in conditions where the characteristics of the spell cannot be made to conform, the casting fails and the spell is wasted.
Spells also fail if your concentration is broken and might fail if you're wearing armor while casting a spell with somatic components.
The text about spell failure in the Eldritch Knight ability seems to be there to simply remind the EK that his armor still causes ASF.
Two weapons, not effectively. But releasing your grip on a weapon is a free action and so is returning your grip to a weapon. You can hold a two-handed weapon in one hand, you just can't wield it that way. So, your greatsword wielding EK can attack with his greatsword and, if he crits, release the greatsword with one hand to cast a swift action spell, and then return his hand to the hilt and be ready to attack again.
So I take it no Eldritch Knight can use a two-handed weapon or two weapons at the same time (well, they can, but they couldn't use Spell Critical then), or am I missing something?
That is correct. The easiest way around this is to use a hand-and-a-half sword, like a Bastard Sword with the Exotic Weapon pro. You can't predict spell crit (which is sad) but you can switch seamlessly between one and two handed fighting so you can cast spells. And, if you use Keen Edge to buff your sword, you can just go one-handed for a while, since your chance to crit is greatly increased.
Or, if you happen to crit while using your sword two handed, you can choose to use a spell with no somatic components (which doesn't require a free hand) assuming you have one. I've played a very melee-intensive EK recently, and I learned the hard way about not keeping something like this prepared for just such occasions. Blindness/Deafness, any of the Power Words, Shout (but not Greater Shout, no idea why), Wail of the Banshee, and a smatters of Enchantment spells are pretty much it, but since it's a free action, even a crappy spell can be nice. Think about it - you crit on the enemy and - bam - they're blind. Not as good as hitting them with a crit and a disentegrate, but you get your x1.5 Str to the crit, and on any other attacks you were taking, and it's not like you can predict a nat 20 roll.
@Zelgadas: See above. You can release and grab a weapon as a free action. Holding something only requires that you have the strength score to lift it (which you ought to). Wielding a weapon (that is, being able to attack or threaten with it) requires a requisite number of hands. Since you needn't wield the weapon to cast the spell, you can release it with one hand and cast your spell, then re-grab it with another free action making it ready to wield again.