This is from a group of Muftis in a response to a question regarding disjointed letters in the Qu'ran from Islamonline:
Ibn `Abbas was reported to have said that these letters stand as a proof of the authenticity of the words that occur after them.
In Az-Zamakhsharis Kashshaaf, we read: These letters indirectly denote that though being part of their own language, the Quraysh tribe failed to produce the like of the Quran.
Some scholars adopt the view that these letters are names of the surahs (chapters of the Quran) in which they are mentioned.
In another place, we find that these letters are an aspect of the challenge directed to the disbelievers (to produce the like of the Quran). Although the Prophet (peace and blessings be upon him) was illiterate, he brought something very unique in every aspect.
The eminent Muslim scholar, Dr. `Abdul-Fattah `Ashoor, Professor of the Exegesis of the Qur'an at Al-Azhar Univ., states:
Alif Lam Mim [and the like] are separate or disjointed letters that many Qur'anic surahs start with.
Scholars hold different opinions regarding their meaning. The most correct opinion is that Allah refers to the fact that the Quran consists of the like of these letters. The People of Quraysh were challenged to produce the like of the Quran, which is of Arabic letters, and they failed to produce its like. They failed to produce 10 surahs, a single surah, or even a verse.
This sheds light on the fact that the Qur'an is revealed by Allah. No one can produce it, even the Prophet himself who was an eloquent man.
Allah Almighty says: "Say: Verily, though mankind and the Jinn should assemble to produce the like of this Quran, they could not produce the like thereof though they were helpers one of another." (Al-Isra': 88)
This is where the challenge is being talked of in past tense and that this challenge was meant for the Quaraish 1400 years ago,this is the only logical conclusion IMO