2) A dialogue between McCoy, Carmichael and Schiff (spoilers on
"Panic" if you ain't seen it yet):
   Carmichael: We had the right motive but the wrong outraged spouse
   Schiff: Assumption, or can you prove it?
   McCoy: Cut and dried.
   Schiff: J. Edgar Hoover would be proud. Do what you have to do.
I do not understand the reference to former US President Hoover. I
assume the line "Cut and dried" means "We have proof" (it's cut and
dried, so it's as ready as can be). Why on earth Hoover would be
proud of that?
  J. Edgar Hoover was head of the Federal Bureau of Investigation

3) When Briscoe and Green arrest the person whom they think committed
the crime, they read him his rights. But the guy is an FBI agent and
says "I've recited Miranda as many times as you have". Why is the
rights speech called Miranda?
Its based on an 1960s case of State of California (? or NY) vs. an
immigrant named Miranda. He was unclear that he could have kept
his mouth shut and not confessed. He had a smart PD who appealed
and when it got to the U.S. Supreme Court, they overturned his conviction
and made new law, saying certain rights had to be read to every arrestee,
hence the nickname "Miranda".

4) McCoy offers Murder Two to the guy, and he says: "I'll knock five
years off the front end". I was assuming that meant reducing by five
years the maximum of time to be served: however, the guy eventually
gets from 20 to life. And life cannot really be reduced by 5 years,
can it?
He meant from the front of the sentence. 20-life instead of 25-life.
With the parole system, he would have less to serve before he was
eligible for parole.

5) Lastly... As he questions an expert, McCoy says "People's
thirty-five". What does that mean?
People's exhibit 35. In most courts, the exhibits (anything from
murder weapons to paperwork to clothing to tapes) is labeled
People's (or Prosecution) and Defense and then numbers. In
some places, its labeled by letters. So one jurisdiction could say
Defense #12 and another Prosecution H or even BB if there are
more than 26 exhibits.