Pepys' diary relates to us the story of Sir Charles Sidley, who in 1663
exposed himself and purportedly relieved himself on the crowd below. 
The result is essentially the first obscenity trial on record. 

I want to know
   1. The exact date this event occurred
or,
   2. The exact date of the conviction
or,
   3. Both!

This is not particularly easy to find.

ftp://ibiblio.org/pub/docs/books/gutenberg/etext03/sp30g10.txt
pepys' diary july 1 1663
Thence by water with Sir W. Batten to Trinity
House, there to dine with him, which we did; and after dinner we fell
talking, Sir J. Minnes, Mr. Batten and I; Mr. Batten telling us of a late
triall of Sir Charles Sydly  the other day, before my Lord Chief Justice
Foster and the whole bench, for his debauchery a little while since at
Oxford Kate's,
coming in open day into the Balcone and showed his nakedness, .  .  .  .
and abusing of scripture and as it were from thence preaching a
mountebank sermon from the pulpit, saying that there he had to sell such
a powder as should make all the [women] in town run after him, 1000
people standing underneath to see and hear him, and that being done he
took a glass of wine .  .  .  .  and then drank it off, and then took
another and drank the King's health.  It seems my Lord and the rest of
the judges did all of them round give him a most high reproof; my Lord
Chief justice saying, that it was for him, and such wicked wretches as he
was, that God's anger and judgments hung over us, calling him sirrah many
times.  It's said they have bound him to his good behaviour (there being
no law against him for it) in L5000.

Legal reference to this case:
n3 (1663) 1 Keb 620, 1 Sid 168; see 17State Tr 155, Pepys's Diary, 1st July 1663

Dear soylent,

     Thank you for your very intriguing question about a quite interesting 
event.  It appears, however, that the exact date of neither the trial nor the 
conviction is certain.  The citations you provided were very helpful in 
distinguishing the most bona fide sources regarding this case. Neither the 
Keble book (1 Keb 620 1663), nor the English Report (vol.83 Eng.Rep.1146), 
which lists a replication of the official record of the case, provides an exact 
date.  I confirmed this with the UC Hastings Law Library reference librarian 
who pulled the actual documents from their archives.  This library can be 
contacted at 

http://www.uchastings.edu/library/

and their reference desk can be reached at (415) 565-4751.  References of this 
case are found in the Supreme Court Cases, Memoirs vs. Massachusetts 383US 413 
(1966), and United States v. 12,200-Ft. Reels of Film, 413US 123 (1973).  In 
the former case, Justice Douglass writes the following excerpt:
“Nor is there any basis in the legal history antedating the First Amendment for 
the creation of an obscenity exception. Memoirs v. Massachusetts, 383 U.S. 413, 
424 (DOUGLAS, J., concurring). The first reported case involving obscene 
conduct was not until 1663. There, the defendant was fined for "shewing himself 
naked in a balkony, and throwing down bottles (pist in) vi & armis among the 
people in Convent Garden, contra pacem, and to the scandal of the Government." 
Sir Charles Sydlyes Case, 83 Eng. Rep. 1146-1147 (K. B. 1663). Rather than 
being a fountainhead for a body of law proscribing obscene literature, later 
courts viewed this case simply as an instance of assault, criminal breach of 
the peace, or indecent exposure. E. g., Bradlaugh v. Queen, L. R. 3 Q. B. 569, 
634 (1878); Rex v. Curl, 93 Eng. Rep. 849, 851 (K. B. 1727) (Fortescue, J., 
dissenting).”

FindLaw.com:
http://caselaw.lp.findlaw.com/scripts/getcase.plnavby=case&court=us&vol=383&page
=413.

In the latter case, United States v. 12,200-Ft. Reels of Film, 413US 123 
(1973), the following excerpt is written in the footnotes:
“The Sir Charles Sydlyes Case, 1 Keble 620 (K. B. 1663). . . made a public 
appearance on a London balcony while nude, intoxicated, and talkative. He 
delivered a lengthy speech to the assembled crowd, uttered profanity, and 
hurled bottles containing what was later described as an "offensive liquor" 
upon the crowd. The proximate source of the "offensive liquor" appears to have 
been Sir Charles. Alpert, Judicial Censorship of Obscene Literature, 52 Harv. 
L. Rev. 40-43 (1938).” 

FindLaw.com:
http://caselaw.lp.findlaw.com/scripts/getcase.pl?
navby=case&court=us&vol=413&page=123.

Through my research I believe it is justified to conclude that the exact date 
of the trial and verdict in The King vs. Sir Charles Sidley is not published, 
nor precisely known. 

Additional Websites that may interest you:
 
Findlaw.com – U.S. Supreme Court obscenity cases.
http://www.findlaw.com/01topics/06constitutional/cases.html

Findlaw.com – recent U.S. Supreme Court Cases. 
http://www.findlaw.com/casecode/supreme.html

Galaxy.com – a list of U.S. law libraries
http://www.galaxy.com/hytelnet/US000LAW.html


Search Terms Used: 
Sidley
Sydlyes
The King vs. Sir Charles Sidley
Pepys’ Diary

The closest I've come to finding a date for this fascinating incident is at 
http://www.thefileroom.org/FileRoom/publication/atkinshistory.html

This gives the date of the offense as June, 1663. This makes sense as far as 
the British climate is concerned - you'd have to be very drunk to go naked in 
Covent Garden in, say, April - but it seems like an astonishingly short time 
for the case to go to court.

If Pepys was recording the event as happening 'the other day' in July of '63, 
then there must have only been at most a few weeks between arrest and trial, 
which sounds ridiculous to me. Still, I'm no expert in seventeenth century law, 
I'm afraid.

There are some more lurid details - which Pepys is too prudish (?) to mention - 
at http://www.wvu.edu/~wvjolt/Arch/Saunde/Saunde.htm