I think it's great your pastor is taking you through the different end-times views. It shows a mature approach that is willing to open the scripture and allow other believers to challenge us with insights they may have that we never thought of. Basically, my rejection of dispensationalism can be reduced to three main objections:
1) With the once-for-all sacrifice of Jesus Christ, there can no longer be animal sacrifices. Furthermore, the whole levitical priesthood and ministry has been replaced by Christ's priesthood and ministry (see Heb. 7-10). Therefore, there can never be a revival of the OT system during a future millennium.
2) Jews and Gentiles have been brought into "one new man", which is the Church or the Body of Christ, through Christ's work of redemption. There is now no more enmity between the two (see Eph. 2:11-22). Therefore, the dispensationalists wrongly teach that there are still (or can ever be again) two peoples of God. Only a reversal of Christ's cross-work could make such a situation thinkable.
3) No matter how many "dispensations" different dispensational writers think there are, the pre-determined pattern is always the same: man is given responsibility, he fails, and judgment must inevitably follow. However, Jesus Christ did not fail. He broke the cycle of human failure and made possible true obedience. This is the promise of the new covenant (Jer. 31 and other passages), that God will pour out his Spirit and give his people hearts of flesh so they will be empowered to render obedience to him. Contrary to Scripture, dispensationalists teach that the new covenant has not been established (Matt. 26:28) and that the gates of hell do in fact prevail against the church (Matt. 16:18)!
Now, I don't know the future. Sin will always be a fact of the human condition until Christ returns. However, it is a lack of faith that says the conversion of culture is impossible. It is also unhistorical. We have already had over a 1000 years of Christendom. The "Dark Ages" is simply propaganda devised by Enlightenment historians. During that period, western Europe outpaced all other civilizations in cultural, scientific, moral, and spiritual development. The problem was, as I see it, that we had so much success that later generations took it for granted and forgot Who's blessing made it all possible. So the last 200 years or so of apostasy, and the last 100 years of the worst bloodshed in human history, may be bringing us back to the realization that the nations must repent if they expect to prosper with God's blessing (Ps.2).
I am hopeful but not certain of what the future may bring. From the human perspective, we must strive to obedient to God's word regardless of the outcome. This means that society as a whole, and not just individuals, are obliged to bow the knee to Jesus, who has been enthroned as King of kings and Lord of lords (Phil. 2:8-11).
One last thought, _____. There is no biblical promise anywhere that Christians will avoid suffering in this world. In fact, we have been told to expect persecution. As far as the judgments that God will pour out on the world, the Israelites were not raptured out of Egypt during the plague judgments. God was able to preserve his people while visiting wrath upon the Egyptians. Similarly, the rapture is not a necessary prerequisite for the Great Tribulation to occur. Of course, I do not deny the future resurrection; I merely differ with my dispensational brethren on the proper sequential arrangment of events. Much more serious are the differences I've outlined [above].