Which species present the most problems when trying to visually distinguish between males and females, without a hands-on inspection?
There are lots of species where it is completely impossible to distinguish between male and female without a DNA test or checking an animal's insides.
Can anyone provide some useful examples when the problem is particularly acute for species commonly kept by zoos?
If you want an example that may pose particular problems in zoos, a good example is turacos. As far as I know, the only turaco species that is possible to sex visually is a White-bellied Go-away Bird. I believe all other species require being sexed genetically or surgically.
Giant Panda (*cough* Zoo Atlanta, who got three cubs wrong in a row!) Aardvarks - despite DNA tests now being standard practice for youngsters mistakes are still made