"The Real Book About Crime Detection" (1957): 4 Ridiculous Gun Stances or Disarm Your Target By Making Them Laugh

"The first man standing is sighting through the reflection in his ring"

Why couldn't he just swivel his head a bit to face the target? Your average man's ring is not going to be big or shiny enough to use to aim a gun accurately.  Unless it is Lady Gaga or Elton John, your average person is not going to walk around with a giant mirror ring.  It also seems irresponsible to just fire a gun based on a small, blurred image which might or might not be your target.

"The second man standing is viewing the target through a mirror held between his knees"

When would this happen?  Did detectives travel with small hand mirrors?  It seems like it would take a long time to get the mirror in the right position between the knees. 

This is a far cry from glamorous detectives/agents like James Bond.  The first guy looks like he is checking his nails and the second guy looks like he is doubled over with cramps.