Maybe you could clarify a few things for me

it will only work in desktop.

I seem to recall some BBC faq about desktop settings but can not find it at the moment. Have you got a link to that faq or whatever you found ?
Desktop is a very common term in iPlayer posts due to one of the embeded players being called iPlayer desktop.

When you say

it works fine with chrome and other browsers 

Are you referring to use of iPlayer on a laptop or similar device, rather than on your Galaxy Note

The Galaxy Note is not listed as supported, but in the days when they had a forum the faqs often were not updated, and it would not surprise me if that was still the case.

• list http://iplayerhelp.external.bbc.co.uk/help/mobile_iplayer/mobile_phone

it works fine with other browsers, chrome egc on my samsung tablet. iplayer loads mobile version rome the issue appears to be that via firefox iplayer cannot recognise the device as it thinks it is a desktop. Even if I uncheck the request desktop site box it will not load the mobile iplayer. as I have said above it load and works well with chrome on my tablet