Thanks for the note and the question. The Bible Knowledge Commentary has this to say about 1 Samuel 13:1:
13:1 . If the setting of the reaffirmation of Saul’s kingship and Samuel’s address on that occasion is the first anniversary of his coronation, it may be that the events of this chapter occurred after his second anniversary. This is a possible interpretation of the textually difficult passage translated by the NIV as Saul was 30 years old when hebecame king, and he reigned over Israel 42 years. The Hebrew is literally, “Saul was years old when he began to reign and he reigned two years over Israel.” Obviously a figure has dropped out of the first part of the statement, and the second part cannot mean that he reigned for a total of only two years. Old Testament chronology implies—and Paul in his address at Pisidian Antioch (Acts 13:21) distinctly teaches—that Saul reigned for 40 years, no doubt a round number but close to the actual figure. There is no reason to think that the number “two” is suspect, however, for all manuscripts and versions retain it. It is only the desire to see 1 Samuel 13:1 as a regular formula for kingship (as in 2 Sam. 2:10; 5:4; 1 Kings 14:21; 22:42; etc.) that leads many scholars to postulate that “40” or some other figure is missing. In the context, however, the historian is not introducing a kingship formula (why do so here, well into Saul’s reign?), but is probably indicating that the Ammonite threat had come in Saul’s first year and now, in his second, the Philistines must be encountered.
A problem remains with the first part of the Hebrew statement, “Saul was years old. . . .” Many scholars, following Origen (ca. a.d. 185-254), postulate “30” (so niv). Since Jonathan, Saul’s son, was already grown then and served as a military commander, Saul would have been older than 30. It is more likely that the figure to be supplied is “40” though this too is difficult to reconcile with the description (1 Sam. 9:2) that Saul was, at the time of his anointing, “an impressive young man.” Of course “young” in this latter passage may not be a good translation for the Hebrew baµh\uÆr, a word that could be rendered “choice.” The best translation of 13:1 would seem to be, “Saul was  years old when he began to reign, and he reigned over Israel for two years.” This is further supported by the next verse which begins with a verb in the preterite tense, a construction indicating a close connection with the previous clause. “Saul chose . . . ” (v. 2) implies that after he had reigned for two years Saul began to select and train a regular army, not the larger militia he had used previously.
Walvoord, John F., and Zuck, Roy B., The Bible Knowledge Commentary, (Wheaton, Illinois: Scripture Press Publications, Inc.) 1983, 1985.
Let me give a more general answer to this problem and other textual difficulties in the Bible. Our view of inspiration is that God inspired every word of Scripture "in the original manuscripts." We don't have any original manuscripts, though we have many ancient manuscripts that are very reliable. There are differences in the manuscripts, as we should expect in texts that are hand copied. The problem in 1 Samuel 13:1 may simply be that a copyist left a word out. Because I believe in the inspiration and inerrancy of the original manuscripts, I am assured that if the missing (or corrupted) word that was in the original manuscript were known, most of my problems would be solved. Just being assured that there was an original inspired and inerrant manuscript encourages me to seek to discern what it might have been. The fact that some of the copies we have in hand have minor inconsistencies does not cause me to lose faith in my Bible; it does require more study. And where the answer is not readily apparent, I simply wait till that time when our Lord can explain it to me.
In addition, there are apparent discrepancies or contradictions. How could the promised Savior be both man and God? How could the coming Messiah both be rejected and suffer at the hands of wicked men, and also come to the earth in triumph and victory? The solution is Christ. But before His coming, men scratched their heads as to how the Scriptures could be true. (see 1 Peter 1:10-12)