What kind of listening devices were used during the fifties and early sixties to pick up private conversations?
Were any wireless?
Interestingly, the basic techniques for moving sound from one place to another has not changed much since this time. Just the instrumentation has changed. Reason... snatching sound is basically a physics problem, and those laws were written long ago.
In the 50's and 60's telephone wiretapping was still simply a matter of, well... tapping the wires. The tap could continue to the listening post via a wire path (most likely) or be transmitted via radio. Room conversations were also snatched in a similar manner... a microphone in the room, with the path to the listening post being wired or wireless. Surveillance radio transmitters in those days used "peanut" tubes, and later transistors. Many how-to articles were published in the hobbyist magazines of the time.
One of the most famous eavesdrops of the time involved a bug built into The Great Seal of the United States, given as a gift by the USSR to our ambassador in Moscow. It used reflected microwave energy to carry sound from the ambassador's office.
For more information related to your question...
Visit our Great Seal Bug page.
For more eavesdropping history visit our history section.
Search the used book stores for a copy of...
The Electronic Invasion, by Robert M. Brown (the 1967 version) Library of Congress card catalog # 67-21759, John F. Rider Publisher, Inc. / Hayden Publishing.
The ultimate full-color text on spy tools is (of course) The Ultimate Spy Book, by H. Keith Melton, 1996, DK Publishing, Inc., ISBN-0-7894-0443-5
Kevin