Explain why the colonists objected to such things as writs of assistance and vice-admiralty courts.

The basic reason for this is that these things gave too
much power to British law enforcement agents and reduced the colonists' rights in the
judicial system.

Writs of assistance were essentially
general search warrants that allowed an officer to search a place at any time to look
for evidence of crime.  The vice-admiralty courts were courts (located outside the
colonies in Halifax) that had no juries to try accused criminals.  When combined, these
two types of things took away many of the rights that the colonists wanted.  These types
of things made it easier to find evidence of crime and easier to convict accused people
(because a judge appointed by the government would be more likely to convict than a jury
from a particular colony).  This is why the colonists disliked such
things.