Using Lightroom's Search Filters
Use the Library Filter for just Date, and turn off all the others (set to None)
Lightroom will display the photos sequentially, using the Camera's EXIF Data for "Time Captured" by Month, day, year and hours, minutes and seconds. Any photos with the same Capture time will be displayed side by side...
It would look like this in Lightroom's Library Module...
Things to watch for are photos shot with a hi-speed "burst" shooting Mode where 3 or more photos are less than seconds apart. It would be best if you stacked photos shot in a rapid sequence, or bracket first.
You can also try a search by Filename, and use as a filter Contains = "copy", or "1" or "2" ... sometimes when files are duplicated one of those extensions are added to the filename...
Plug-ins
Before you use or try any of these plug-ins, make sure your catalogue is up to date, optimized and backed up...
Teekesselchen
A FREE fast duplicate finder plug-in for Adobe Lightroom using EXIF meta-data.
http://www.bungenstock.de/teekesselchen/
I was really impressed with how fast this plug-in worked and how it is implemented. The online documentation is excellent.
LR Duplicate Finder
A "commercial" plug-in by Jim Keier (England) Cost is £8.50 (currently about $13.50 in US Dollars
You can watch a video and purchase it on this page http://www.lightroom-plugins.com/DupesIndex.php
Laura Shoe, a Lightroom Guru also has a video with some useful insights, you can watch it right here!
Stand Alone Programs for Mac and PC
Mac
My favorite Mac duplicate finder Photo app is called PhotoSweeper
There is a Lite version http://overmacs.com/photosweeperlite.html $2.99<br >
and a "Full" Version. http://overmacs.com/photosweeperlite.html<br > $9.99<br >
The PhotoSweepers work on iPhoto, Aperture and Lightroom Libraries. At the above websites you can even download a trial version.
PC
Awesome Duplicate Photo Finder
A free Tool for finding and remove duplicate photos on your PC. http://www.duplicate-finder.com/photo.html