This is more a description of my troubleshooting efforts. IM logs between Magnus (Lodin333 Resident) attached with his permission. Note that I have also filed a trouble ticket (#2284832), and will update it with this JIRA reference.
Magnus IMd me this morning to request a new group role. The group is "Horsegirls of Second Life" (group UUID 2e54b0bf-6ae3-b6fb-c6c8-c4d369cf26fd). I created this group and am the only person with the owner role in the group. At present the group is set to allow membership to be visible to all, including non-group members. I was logged in using the Firestorm 7.1.11.76946 viewer at the time. I pulled up the membership list on the General tab and did not see him in it. I then went to the Members & Roles tab, clicked on the "Members" sub-tab, and typed his name into the search bar, and got "No match."
I asked him to take a screenshot of the group profile with his membership role, etc. and send it to me, but he didn't know how to take a screenshot, so I sent a group notice and asked him if he received it. He confirmed he received it by cut-n-pasting the text of the notice back to me in IM. My Firestorm viewer settings are to echo notices to the group chat, which I had open, and I confirmed that way that the notice had indeed gone out to the group. For reference, the notice was sent at 09:51:56 SLT, the title was ""Test notice", text was "This is a test notice for Magnus (Lodin333 Resident) to see if his group membership is working properly."
At this point I wanted to see if it could possibly be viewer-related, so I logged off, went to the SecondLife website and downloaded the most current version of the official viewer (SecondLife Viewer 7.1.10.10800445603 - DeltaFPS), installed it, and logged in to resume communication with Magnus.
Again, I opened the group profile and looked through the members listed on the General tab; I did not see his name. I went to the "Roles & Members" tab, opened the Members sub-tab, and entered his display name, then his account name in the search bar, and got "No match" as a result each time.
I then repeated the notices technique; he received the second notice and echoed the text back to me. For reference, the second notice was sent at 10:06 SLT; the title was "Test notice #2", text was "This is for Magnus again and this is test notice #2." Both notices are available in the group notice history
To close, I have noted similar behaviour in other groups of which I'm a member, including 4 in which I am an officer, with most of the group powers assigned. However I don't know for certain what some of those groups' settings might be as I am not the owner nor did I create them. Since I am also experiencing this problem in a group I created and own, I felt this was the best one to use for a JIRA bug report.