How does Zeffirelli deal with the problem that led to the heated debate during the following centuries in his film on Hamlet?

There have been, over the centuries, many heated debates
about the play Hamlet.  You might be referring the the question of
Hamlet's Oedipal Complex and how Zeffirelli plays up  the possibility of sexual
attraction between Gertrude and Hamlet, but I will discuss the controversy surrounding
the text of Hamlet and how Zeffirelli addresses
that.

Much of the controversy stems from the fact that
there are so many "versions" of the script.  If one staged (or filmed) all the material
that exists of Hamlet, it woud take 4 to 6 hours to perform.  There
are scenes (depending on Quarto or Folio consulted) in different order, additional text,
lines attributed to different characters -- all of which have led to confusion and
questions about the "real" script of the play.

As
Zeffirelli did with his filmed productions of some Shakespeare's other plays
(Romeo and Juliet being the first and arguably the most
significant), he dramatically edited the text.  For his film version of
Hamlet, he arranged scenes and soliloquies in the order in which
they served the story he wanted to tell, not based upon the most common order of
presentation.  The whole film runs a breezy two hours fifteen minutes, and is quite easy
to watch and understand.

This approach to adapting
Shakespeare for film with a strong emphasis on reduding the running of time of each
scene, so that the story moves in a cinematic fashion rather than a theatrical one, was
an innovation that Zeffirelli can be attributed with initiating.  For my money, though
his setting and costumes choices were not "modern,"  he was certainly the
ground-breaking filmmaker who paved the way for films like Romeo +
Juliet and the version of Hamlet starring Ethan Hawke --
films that keep the text 100% Shakespeare, but shape the story to suit a modern
film-goer's sensibilities.