Stephen Dillane is severly over-shadowed by his co-star Mel Gibson. Zeffirelli seemed in favor of cutting Horatio's lines in order to give Gibson more screen time. 

One example of this is Hamlet's death scene at the end of the play. Horatio is supposed to say, "Now cracks a noble heart. Good night, sweet Prince, And flights of angels sing thee to thy rest" (V.ii. 358-360). Instead, Zeffirelli cuts "Now cracks a noble heart," and ends the play after line 360, not exactly redeeming Hamlet.