We have 2 iPhones,2 iPads and a old iPod touch. The phones and iPod can predate the Mac mini using the apple Remote application, but the pad cannot. They submit the PIN which is accepted in iTunes, but after that they report a connection error, meanwhile the other devices sitting next to them are connected (concurrently) fine.
Note, all devices are using the same iTunes account.
I have had issues with the Remote app and that can not connect message before. It turned out it was my wireless router causing the issue - when I replaced it, the problems all went away. We have about 5 devices using remote.