[Problem]
A WLAN did work for some devices (notebooks, tablets, ...) but not for all. Default checks brought nothing - we made sure there is no channel crowding or a particular strong wireless network close that 'shouts' over all others and also used a WLAN repeater so reception wouldn't be an issue. Of course we also checked type of encryption and if all devices should work (which was the case with the default WPA2). There also was no good error message at all, most devices that did not work simply stated "could not connect" or times out. The primary problem was a WLAN controllable air-conditioner (brand 'Daikin')
[Solutions]
That was a tough one to debug remotely - because in the end, the SSID was the issue. It contained a special char (a german Umlaut). The SSID was something like 'Kühlschrank' which caused problems for some devices that would not allow for special characters in an SSID and simply not connect without any meaningful error message. The SSID was changed to something that contained only alpha-numeric chars and the devices not working before could finally connect!