Well, most of them are pre-tribulationist; heavy rapture theology controls the majority of their doctrinal approaches.
Another note is their inclination towards the gifts of prophesy and their interpretation of glossalalia. Their teaching on the Holy Spirit and the gifts of the Holy Spirit is held in high regard, almost as if it is parallal to the Sacred Scripture. Their passion for a spiritual word from God, even when it contradicts Sacred Scripture overrides doctrinal teaching at times. It is interesting to note that when someone "receives" a prophetic word from God and spoken in a service aloud, that this prophesy is given as a forecoming of either events to come, a healing, a restoration of some sort or a caution for someone to take heed to. This type of service is very emotional and the passions are extremely indulged by the sense of something very spiritual. This type of service attracts those who have never felt the presence of God nor have partaken of the Mysteries of Christ.
Foursquare is a emotional rollercoaster. The service are extremely emotional, very massive in its worship services which include modern music, very "charismatic" i.e. lifting up of hands, tongue speaking at times, even singing in tongues, and is led by either the Pastor or the music director who leads the congregation through hypnotic words and emotionally driven music. It can be a drug, an opiate of the masses. After this worship service comes the Pastoral teaching(Sola-Scriptura, Arminianist mostly, some Calvinism, its really a mixture of what feels right for each individual) and then a closing worship time afterwards. This is typically seen in most cases as the norm.
Many people are devoted to this because it gives them a sense of being personal with God, the feeling of being able to stand before God and bow down at His feet as many of the songs sang in the movement speak of doing such things.
I can only tell you my experiences with it, as I left it almost ten years ago and I had no congregation I was in charge of at the time I left.