While I remember enjoying reading this series when it first came out, that was before I had spent much time studying Biblical Interpretation and Theology. At the time I didn't think I agreed with the way the authors were interpreting Scripture, but I didn't have much to go on.
The Left Behind Series is based on an extremely literal rendering of passages of scripture in the Bible, especially apocalyptic texts. People who embrace this interpretation of the text (premillennial dispensationalism) must be unaware or or choosing to ignore the fact that apocalyptic texts are known for using highly symbolic language to communicate truth and must be interpreted in light of the larger framework of the Judeo-Christian worldview. (Example: The plagues mentioned in Revelation echo the plagues in Exodus where God was rescuing his people and judging their oppressors.)
N. T. Wright said the dramatic end-time scenario of believers being snatched up into heaven is an incorrect interpretation of 1 Thessalonians 4:16-17. That passage about meeting the Lord in the air "should be read with the assumption that the people will immediately turn around and lead the Lord back to the newly remade world" -- similar to residents meeting a visiting emperor in open country, then escorting him into the city. Jesus never predicted such an event. "The gospel passages about “the Son of Man coming on the clouds” (Mark 13:26, 14:62, for example) are about Jesus’ vindication, his “coming” to heaven from earth. The parables about a returning king or master (for example, Luke 19:11-27) were originally about God returning to Jerusalem, not about Jesus returning to earth. This, Jesus seemed to believe, was an event within space-time history, not one that would end it forever."
- N.T. Wright