Well. I have now found a solution. As storage is cheap I will copy my post from over on the Mint forum:
To summarize the issue... I installed Mint 13 Mate and allowed it to download and install the Broadcomm driver. I tried to create the wireless connection using mate-network-admin
(Networking app from the Menu; Administration). This created entries in /etc/network/interfaces which caused issues on boot. I confirmed that the identical Broadcomm driver worked OK on Mint 13 Cinnamon and Ubuntu 12.04 (from which Mint 13 is derived). Here step by step is how I managed to get wireless networking working on Mint 13 Mate:
1 - Connected the netbook to my router by an Ethernet cable
2 - Performed a clean install of Mint 13 Mate
3 - Had a look at the network situation as follows
Right click on the network icon in the notification area (which is nm-applet) and observed the following
Enable Networking was checked
Enable Wireless was checked
Connection Information showed me the details of the wired connection
Edit Connections took me to a dialog which showed
Wired tab - Wired connection 1 present
Wireless tab - no entries
4 - From the Menu; Preferences; Additional Drivers I downloaded and installed the Broadcomm driver. For reference the file is bcmwl-kernel-source_188.8.131.52+bdcom-0ubuntu6.1_i386.deb
5 - Rebooted to complete the installation of the driver.
6 - Right clicked on the network icon in the notification area and selected Edit connections.
7 - Selected the Wireless tab and pressed the + Add button. I supplied the following data
Connection name" Wireless connection 1" (the default which was shown)
SSID: Luca$Electric (the name of my router - British car fans will understand this
) This is not broadcast by the router
I moved to the Wireless Security tab and set:
Security: WPA and WPA2 Personal
Password: (the appropriate password for my router/network)
Finally I saved the connection and closed the dialogs. I still did not have a connection. So...
8 - I again Right Clicked on the network icon in the notification area and this time I clicked Connect to hidden wireless network
Behold - I was connected!!!
9 - Disconnected the Ethernet cable and rebooted. I was again and automagically connected to my wireless network.
n.b. The option to "Connect to hidden wireless network" is no longer present when I right click on the network icon in the notification area.
If you are having trouble connecting a Broadcomm or any other wireless card in Mint 13 Mate consider trying these steps. Do NOT use the Menu; Administration; Network program. It doesn't work and thinking back it does not work in Ubuntu either going back at least to 9.04.
Hope this helps someone.