The biggest error of dispensationalists is the confusion over who is Israel. The New Testament uses the term “the Israel of God” (Galatians 6:16). How is this different from Old Covenant Israel? Answer: The Israel of God is no longer ethnic Israel. Believers in Christ, that is the church (including both Jewish and Gentile believers) are the new spiritual Israel through faith—the Israel of God.
Jesus told the Jewish leaders of his day that the blessings of the covenant kingdom were being taken from them and given to another group—obviously Christians (Matthew 21:33-45). The text says that the Jews knew he was talking about judgment against them. Jesus put an exclamation point on the coming wrath against the Jews in Matthew 23:29-39 in which He declared that ALL THE RIGHTEOUS BLOOD EVER SHED ON EARTH would be judged against THEM (Old Covenant Israel) in THEIR GENERATION.
The Old Testament, beginning with Deuteronomy 28-32, and reiterated numerous times by the prophets, foretold an END to Israel. “THE TIME OF THE END” (Deuteronomy 31:20, 29; Daniel 12:6, 9) would be when the Jews would become so unfaithful that God would take VENGEANCE (Deuteronomy 32:35, 43) and DESTRUCTION (Deuteronomy 28:61-64) on them. This would happen when the “power of the Holy people would come to an end” (Daniel 12:7 and the burnt offering ceased (Daniel 12:11). This was fulfilled in history in AD 70 when Jerusalem and the temple were destroyed.
Their rights to the kingdom of God were always conditional and would be forfeited for unfaithfulness (Deuteronomy 28:1, 9, 15, etc.) in the last days (Deuteronomy 32:29). In Luke 21:22, speaking of his generation, Jesus said that the DAYS OF VENGEANCE had arrived. In Luke 9:41 Jesus proclaimed his Jewish contemporaries to be the faithless and twisted generation prophesied in Deuteronomy 32:5.
Paul, in Romans 11:11-13-26, emphasized the importance of this. The Gentiles were grafted into the line of God’s people, and the unfaithful were “broken off.” Only a remnant (Romans 11:5) who accepted Jesus maintained the covenant lineage through faith (Romans 4; Galatians 3:26-29). Thus, salvation is now open to all who believe (John 3:16; Romans 1:16). There is no longer a distinction between Jew and Gentile (Romans 10:12; Galatians 3:28; Colossians 3:11). This is not “replacement theology” but rather “inclusion theology.”
God’s people are now SPIRITUAL Israel and specifically not fleshly Israel of the Old Testament. The New Testament reiterates this in numerous passages, which you can read for yourself: John 1:11-13; Romans 2:11-29; 9:6-8; Galatians 3:6-8, 29; 4:22-31; 6:14-16; Ephesians 2:11-3:13; Philippians 3:3; Colossians 2:11; 1 Peter 2:9-10 (ref. Exodus 19:5-6).
In Ephesians 2:14-18 we see this statement by Paul, “For He himself is our peace, who has made us both one and has broken down in his flesh the dividing wall of hostility by abolishing the law of commandments and ordinances, that He might create in himself one new man in place of the two, so making peace, and might reconcile us both to God in one body through the cross, thereby killing the hostility. . . . For through Him we both have access to one Spirit to the Father.” Thus, the two covenants became ONE. As put by the Reformation Study Bible, “Christ offered in his own body the final sacrifice to which the temple’s sacrifices merely pointed. The ceremonial laws of the Old Testament that separated Jews and Gentiles are no longer appropriate after their fulfillment in Christ.” 
Biblical Judaism ended in AD 70 when the temple was destroyed. At that time animal sacrifices for sin ended and the priesthood ended forever. The genealogical records were also destroyed. Interestingly, DNA testing shows that the genetic identity of modern Jewish populations is not the same as biblical Judaism.
The old covenant vanished away, replaced by the new covenant (Hebrews 8:1-13), through the perfect sacrifice of the Lamb at the end of the ages (Hebrews 9:1-28). The New Covenant in Christ is eternal (Isaiah 9:6-7; Hebrews 13:20; Revelation 5:13; 11:15; 14:6; etc.).
The land promises to Abraham were fulfilled in Joshua 21:43-45; 23:14-15 (cf. 1 Kings 8:56). The promise of a return to their homeland in Jeremiah 16:15 was fulfilled at their return from the Babylonian captivity in 539 BC. The promise of restoration for Israel in Ezekiel 37:26-27 was ultimately fulfilled in the first century with the everlasting New Covenant of Christ (Hebrews 13:20). The sanctuary of Ezekiel 37:26-27 was replaced by Jesus per Revelation 21:22. Similarly, the promise of restoration in Zechariah 8, 10 was fulfilled in Messiah: Zechariah 12:10; 13:7-9 (ref. Mark 14:27); Zechariah 14:8 (ref. John 4:17; John 7:38, and Revelation 21:6).
Dispensationalists, who teach that the land promises to ethnic Israel are forever, and that the temple will be rebuilt complete with animal sacrifices are reading something into the text that is not there. Worse, they are denigrating the finished work of Christ (Hebrews 10:10).
In Matthew 21:18-22 Jesus curses the fig tree. The Old Testament metaphorically identifies the Israel with a fig tree (Jeremiah 24; Hosea 9:10). Matthew 21:12-17 confirms this metaphor by linking the curse on the fig tree with the cleansing of the temple. This was a PERMANENT CURSE against Old Covenant Judaism (“may no fruit ever come from you again” per Matthew 21:19).
Old Covenant Judaism is not a “branch.” Rather, it is a DEAD TREE: “The axe is already laid at the root of the tree; therefore, every tree that does not bear fruit is cut down and thrown into the fire. “ (Matthew 3:10)
The modern state of Israel is not biblical Judaism and has nothing to do with the promises to Israel. Israel today is not even a religious state. So, 1948 has nothing to do with Bible prophecy. That date was supposed to mark the beginning of the end of all things, and in one generation (40 years, thus by 1988) the culmination of all “end-times” things would happen. But 1988 has come and gone. The tribulation/rapture/end-of-the-world theology has proven to be a cruel hoax. Dispensationalism, however, has reached its own end time. Having been born in 1830 with John Nelson Darby, dispensationalism died in 1988. Like my father used to tell me about a dead snake that is still writhing—it’s dead but it just doesn’t know it yet.
See also my article “Prophecy Questions for Dispensationalists”:
 The Reformation Study Bible, page 1707.