How does Mystic Theurge work as far as feat qualification?
To qualify for a small elemental as an 'Improved Familiar' you need to be arcane caster level 5.
A basic Mystic Theurge who got 3 Wizard & 3 Cleric... could they ever qualify for any of the more advanced Improved Familiars (the elemental for example) without gaining more Wizard levels?
Yes, because the mystic theurge increases your caster level. This seems pretty black and white to me. :)
he adds the level of mystic theurge to the level of whatever other arcane spellcasting class and divine spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly.