Name of old black and white science fiction movie (last 50's or early
60's?). Basic theme; men in trench coats and hats follow others into
public washrooms and only the trench coat guy comes out.  At the end
of the movie the trench coat guys (aliens) are shown to have two small
arms which they use to shrink people with and they stuff them into
little bottles hidden in their trench coats or a suit case.

I believe your movie is "Wild, Wild Planet," in which people are
abducted and miniaturized by aliens who wear trench coats and have
extra arms.

Here are some plot descriptions from online reference sources:

"WILD, WILD PLANET... 1965-Italy-dubbed in English

This MGM schlocky sci-fi B-film was made in Italy and dubbed in
English. Italian director Antonio Margheriti ("Castle of Blood") used
the pseudonym of Anthony Dawson to Anglicize his name. The alien
abduction tale goes for high-camp and that Flash Gordon look, but is
such a loser that its nonsense tale never amounts to more than a
robotic romp in outer space and misses the fun in the Flash serials by
light years.

The story is set in the future--2015; the uniform of the day is some
kind of bland pajamas look; the slave of the day is an android; the
transportation system is built around a monorail in a cityscape
setting, as the travelers fly around in cars with fins hanging from
wires. The plot centers around mini-skirted women (a homage to 1960s
pop-culture) with enormous strength, accompanied by robotic
bald-headed men in dark wraparound sunglasses and black rainslickers
that conceal four sets of arms, who shrink people into miniaturized
humans and then tote them in suitcases."

Ozus' World: WILD, WILD PLANET
http://www.sover.net/~ozus/wildwildplanet.htm

"Wild Wild Planet...

The Freaks - Monstrous beings with four arms and pupils like a cat.
Tasked with carrying out abductions on Earth, they are meant to be
inconspicuous. Everyone dresses in bright and flowing clothes, but
these goons wear long black trench coats, black caps, and dark
sunglasses."

Bad Movies: Review for Wild, Wild Planet
http://www.badmovies.org/movies/wildplanet/

"A movie that had strange guys in trenchcoats, hats and dark
sunglasses going around and shrinking people by pinching them on the
neck then stuffing the vacated clothing into a satchel... I'm 99% sure
it's WILD WILD PLANET, an Italian sci-fi film released to the US in
1967."

Tulsa TV Memories: Guestbook
http://tulsatvmemories.com/gb012802.html

"Androids with four arms! Curvaceous, lifelike inflatable women! Bald
interplanetary kidnappers dressed in dark raincoats and shades... The
outrageous premise has Dr. Nurmi (Massimo Serato) attempting to create
a race of super beings on Delphos, a planet owned by 'The
Corporation.' To achieve this goal, Nurmi has instructed his minions
to kidnap top scientists and athletes from Earth for experiments. The
abductions, which are accomplished by shrinking the victims and
placing them in specially created suitcases, are soon traced to
Delphos... one of the kidnappings goes awry and the victim is only
partially shrunk, rendering him a midget."

Turner Classic Movies: Wild, Wild Planet
http://www.tcm.turner.com/ThisMonth/Article/0,,363%7C1221%7C443,00.html

Note that, on the Turner Classic Movies page, it is announced that
"Wild, Wild Planet" will be shown on TCM at the following times next
month:

Friday  10/14/2005 01:15 PM (Eastern)
Tuesday 10/18/2005 11:00 PM (Eastern)

My Google search strategy:

Google Web Search: "wild wild planet" OR "criminali della galassia" 
://www.google.com/search?hl=en&q=%22wild+wild+planet%22+OR+%22criminali+della+galassia%22

I hope this is the correct movie! If it is not, please request
clarification, and I'll gladly resume the quest.

Best regards,
pinkfreud

I have been looking for the title for 2 years.  Thanks a million.