Many people believe that there are gaps in the Genealogy listed in Matthew. This article addresses "the primary problems of the Genealogy in Matthew", and lists the gaps as one of the arguments for "unreliability" leveled by critics.
Section I: What Are The Primary Problems Associated With Matthew’s
Genealogy And How Are They Reconciled?
There are 3 main problems associated with Matthew’s genealogy that
most critics point out. They are as follows:
The Inference That Joseph Was Actually Jesus’ Father
The Promise Of God Against Jeconiah Nullified That The Messiah Would Be As A Result Of His Bloodline. (Jer. 22:29-30)
Too Many Gaps In The Genealogical Succession Of Matthew Against Known References In Other Texts Prove Discrepancies.
The "gaps are explained thus:
The critic often levies the charge that gaps found within the
genealogy of Matthew are as a matter of sloppy investigations of the
facts and proof that Matthew either made the story up or simply
couldn’t seem to get it right even after he wrote it. These type of
statements usually claim the historical ignorance of the gospel writer
and relegate Jesus to the realm of myth, which is another tired
critical argument refuted over and over down through the last couple
of centuries. Was Matthew eagerly, erroneously and fallaciously
promoting information that even he couldn’t seem to get straight? What
are we to make of gaps in Matthew’s account?
Once again this type of observation is clearly and certainly
overemphasized, and has no bearing on the accuracy of the narrative.
It is a fact that some of the individuals Matthew says “begat”, were
grandfathers and sometime great grandfathers and not paternal fathers
and sons. One such example is Mt. 1:8 where Joram is said to have
“begat” Uzziah. We know that 1 Chron. 3:10-12 states that Joram was
Uzziah’s great-grandfather not paternal father. 3 generations are
skipped by Matthew in this case.
The article does go on further, but from just this last paragraph, we can see that this author, at least, believes that there are gaps, and the genealogy is not complete. This has been my understanding as well, as it's a common explanation in Apologetic literature.