The Hebrew text underlying the KJV is reliable and does not have any demonstrable error. By God’s grace and providence there are not as many variant readings among the Hebrew Old Testament manuscripts as there are among the Greek New Testament manuscripts. Most of the variants concern pronunciations which do not affect translation. The KJV is based on the Masoretic Hebrew text edited by Jacob Ben Chayyim, exhibited in Daniel Bomberg's Rabbinical Bible of 1525. Many recent versions of the Bible are based on the Biblia Hebraica Stuttgartensia, the third edition of the Masoretic text edited by Rudolph Kittel. There are eight places where differences between the two texts affect translation – they are: 1 Kings 20:38, Proverbs 8:16, Isaiah 10:16, Isaiah 27:2, Isaiah 38:14, Ezekiel 30:18, Zephaniah 3:15, and Malachi 1:12.
Many modern scholars feel compelled to consult these other sources because of their perceived flaws with the Masoretic text. It follows that these scholars do not believe in the existence of any perfectly preserved Hebrew text. For more on this, please read: Question: Aren't some Textus Receptus readings based on little or no Greek manuscript evidence?. A careful study, however, will reveal that there are no demonstrable flaws with the Masoretic text.
With only eight significant variants between the Jacob Ben Chayyim and the Rudolph Kittel editions, the Hebrew texts underlying the KJV and modern translations are fairly similar. However, modern textual critics believe that all editions of the Masoretic text suffer from various copyist errors. These critics believe that a Bible translation must consult the Masoretic text as well as other ancient witnesses such as the Dead Sea Scrolls, Samaritan Pentateuch, Aramaic Targum, Septuagint, and the Latin Vulgate. The prefaces of some of the leading translations have the following to say about the translators' view of a deficient Masoretic text:
“The translators also consulted the more important early versions – the Septuagint; Aquila, Symmachus and Theodotion; the Vulgate; the Syriac Peshitta; the Targums; and for the Psalms the Juxta Hebraica of Jerome. Readings from these versions were occasionally followed where the Masoretic Text seemed doubtful and where accepted principles of textual criticism showed that one or more of these textual witnesses appeared to provide the correct reading.”
“In exceptional, difficult cases, the Dead Sea Scrolls, the Septuagint, the Samaritan Pentateuch, the Syriac Peshitta, the Latin Vulgate, and other sources were consulted to shed possible light on the text, or if necessary, to support a divergence from the Masoretic text.”
“In the present translation the latest edition of Rudolf Kittel’s Biblia Hebraica has been employed together with the most recent light from lexicography, cognate languages, and the Dead Sea Scrolls” (The NASB then lists these witnesses of cognate languages under its Abbreviations page: Aramaic, Septuagint, Latin, Syriac)"
The following is a place where critics believe that the New Testament author preferred the Septuagint reading over the Masoretic text reading. The link will take you to a separate page describing why the author was not preferring the Septuagint reading over the Masoretic text reading:
Having considered the above, there is no reason to question the reliability of the Hebrew text underlying the KJV.