Which things to consider to test a mobile application through black box technique?

Not sure how your device/server is to operate, so mold these ideas to fit your app.
Some highlights are:
Range testing: Ensure that you can reconnect when leaving and returning back into range.
Port/IP/firewall testing：change ports and ips to ensure that you can connect and disconnect. modify the firewall to shutoff the connection.
Multiple devices： make sure that a user receives his messages with other devices connected to the same ip/port. Your app should have a method to determine which device/user sent the message and only return to it. Should be in the message string sent and received. Unless you have conferencing capabilities within the application.
Cycle the power of the server and watch the mobile unit reconnect automatically.
Mobile unit sends a message and then power off the unit, when powering back on and reconnecting, ensure that the message is returned to the mobile unit.
If you are working with WAP then you can download simulators from net and start testing over it.