It is a common problem for the Dell Inspiron Laptops using Broadcom 43142 (BCM43142) network card not to see wireless networks on Ubuntu 12.10.
But this can be solved in a few steps:
1. Download the Broadcom 43142 driver:
$ wget http://jas.gemnetworks.com/debian/pool/main/w/wireless-bcm43142/wireless-bcm43142-dkms_18.104.22.168-1_amd64.deb
2. Install the needed dependencies:
$ sudo apt-get install linux-headers-generic build-essential dkms
3. Install the downloaded BCM43142 driver:
$ sudo dpkg -i wireless-bcm43142-dkms_22.214.171.124-1_amd64.deb
This tutorial solved the wireless problem on Dell Inspiron 5520 and Dell Inspiron 5720.
Note: The driver I linked in the article is for 64 bit sytems (x86_64). To make it work on 32 bit systems, install ia32-libs:
$ sudo apt-get install ia32-libs
I am not sure that after installing ia32-libs, everything will work perfect, but you can try.