I downloaded a sim from the exchange, and it said it was installed, so I went into the Create-A-Sim and it wasn't in there, even when I picked to only show custom content. It was also not in the bin. When I exit the game, it doesn't show up in my installed content in the launcher, so I made sure I clicked install and waited for the successful install message this time before going back into the game, but I ran into the same problem. --- Now, count up your sins.
I've never had a problem installing a sim from the sim exchange, however there is one thing that may be happening. If the sim was created with some custom content that, for whatever reason, isn't packed with the sim, or was corrupted, then the sim won't display properly. Instead, you'll see a very generic looking sim in the installed sim's place. Worse, if I try to use that sim thinking it'll look the same just with different hair/clothes/whatever, my game will freeze up.
Basically, if you can't see the sim you downloaded, look for a generic looking sim that you didn't install.