Unfortunately, the suggestions have not resolved the problem that I am experiencing. I also have an iPad 2 which does not have any problems with the same Wi-F- connection. From the internet it appears that a fair number of people are having the same problem since doing the latest OS X Mountain Lion update.
The router is fixed on 2,4 GHz as this is the legal frequency in my area. I have already don the update to 10.8.2.
Have done the 10.8.2 (combo) update as suggested without success, with one difference; I now get a message "None of your preferred networks are available", after restarting or rebooting the computer. However, in settings my network is clearly indicated as the preferred network.
Have tried this, but still no luck.
Did this,but could only connect (rejoin) after new setup was done.
I have previously tried the USB Wi-Fi route with the same results. I will probably just have to wait for Apple to come with an update that solves the problem. apple support does not seem very interested in this problem.