Usually people can use a Facebook Graph Search URL with a group ID https://www.facebook.com/search/2204510018/members/2204420210/members/intersect or with a group name https://www.facebook.com/search/str/linux/groups-named/members/str/surfing/groups-named/members/intersect to find people who are in several groups at the same time. One day, I noticed that the URL was not working anymore (it only worked in the mobile version m.facebook.com or in another Facebook account), so I created a script using the Facebook Graph API to display the groups members intersection.
Last time I checked, the URL using a group name was not working. You can find a Facebook group ID in the group URL or in the “Report Group” link.
Update: Unfortunately this script is no longer working since the /group/members edge endpoint was deprecated the 4 April 2018 (reference, changelog, blog post).
Update 2: Graph Search URLs have also been deprecated in June 2019 but it is now possible to use the feature “Members With Things in Common” (URL /members_with_things_in_common) to see members who are in the same groups or city or have mutual friends.
Download script from my server: facebook_graph_api.js