What are the major differences between Hamlet the play and Hamlet the 2000 film version?Especially the differences after Hamlet's mother drinks...

The biggest difference between the play and the 2000 film
of Hamlet is the absence of Fortinbras at the end.  This, however,
is a common elimination in a long play like Hamlet, especially in 
a production (or film) setting the play in a modern
world.

More subtle differences include the elimination of
text, especially text that describes events: "Look to the Queen!"; "They bleed on both
sides."; "She swoons to see them bleed."; etc.  All of these lines are supplanted by
visual images.  In a performance of the play, where an audience must choose where to
look, these lines could be considered necessary, so that each event can attract the
audience's attention.  In a film, the camera chooses for the audience where to look, so
these lines become redundant.

Other alterations to action
that is suggested by the text, has to do with the deaths of Laertes, Hamlet and
Claudius.  In the play, Hamlet is wounded by the poisoned tip of Laertes sword.  He then
manages to get that sword and wound Laertes in return.  Claudius' final demise in the
play comes when Hamlet makes him drink the poison that killed Gertrude ("Drink off this
potion....Follow my mother.").  In the film, in keeping with the modern setting, Laertes
shoots Hamlet, who causes Laertes to fire a second shot that mortally wounds him also,
and then Hamlet shoots Claudius.

The director adds a visual
montage to represent Hamlet's life passing before his eyes as he dies, as
well.

It should be noted that these changes are made
possible in the film without adding any extra text.  The text is still 100%
Shakespeare's words, only some of the non-useful text has been removed.  Editing of
Hamlet, since it's total unedited length can be 4+ hours, is, in
fact quite common.