In William Shakespeare's tragedy Hamlet, Hamlet refers to Polonious as
a "fishmonger." What exactly is he refering to and does Hamlet think
highly of polonious?

Well grade 11 english was a long, long time ago... but I vaguely
recall our teacher pointing out that a fishmonger is a whore? slut?
pimp?... can't really remember, but it's something along those lines.

http://www.clicknotes.com/hamlet/Two2.html#book
http://www.clicknotes.com/hamlet/H22.html#174

Hamlet considers fishmongers (fish sellers?) to be honest men (in his dementia) 

Polonius is the aid to the king who wed Hamlet's mother quite quickly
after Hamlet's father died. I think Polonius would be the only one who
could bear the brunt of Hamlet's agression against the king, but I
think Hamlet doesn't really care what he thinks about Polonius in
Hamlet's state of mind.

As said a fishmonger is someone who sells fish.

Many Hamlet scholars believe Hamlet's madness to be feigned so his
'state of mind' may or may nor be relevant as the debate continues.
Whatever his state of mind, Hamlet is not kind to Polonius. Everything
that Hamlet says to Polonius in that scene is thick with sarcasm and
venom. If he's faking his insanity he's calling Polonius a fishmonger
to make the old man think he is crazy (as he knows Polonius is
checking up on him). If he isn't faking it, then he's just raving mad
in calling him a fishmonger. I prefer the first interpretation since
some of  his soliloquies have him acting rationally (not killing the
King after he has just confessed him sins).

He doesn't outright hate Polonius as he feels some small remorse when
he accidentally kills him, momentarily at least before he goes back
into raving mode. Strong dislike is probably a good characterization
of Hamlet's feelings towards the old coot.