After a long and winding road, and with a lot of research, I managed to stumble on a solution.
The problem is indeed with version 2.262 of Internet@TV, and v2.359 solves the issue. It has nothing to do with the firmware version you have (3006.2, 3007.1 etc), because the firmware updates DO NOT update Internet@TV. The latter is updated separately whenever there is an update available on the Internet@TV servers the TV connects to.
Now from what I reckon, it appears that Samsung have different Internet@TV servers for different countries, and the TV connects to the appropriate server according to the country pre-set at the factory into the TV. Not every country is supported; for those countries that are not listed, the TV Internet@TV country setting is set to 'None'. In this case, the TV connects to a 'generic' server that has very few apps available, and that is not updated as often as the others.
I believe updates of the Internet@TV software is rolled out one region at a time, and this is why some people have later versions of the software than others.
My TV country setting for Internet@TV was set to 'None', which is why the Internet@TV software would not update. I solved the issue by switching the country setting to 'UK', which upgraded my Internet@TV software, solved the issue with Facebook, Youtube, Picasa, and Twitter, installed different default apps, and gave me access to many more services. Please note however, that some services installed, such as BBC iPlayer, will open but will still not work unless you are in the UK, as they check your IP.
Now the question is, how do you change the Internet@TV setting? You do that through the TV's hidden service menu.
These instructions are for the C series (they might work with other series but I have only tried it with the C series, specifically with my UE32C6510 TV). Please be very careful as you may break your TV if you do not know what you are doing. PROCEED AT YOUR OWN RISK!
* Activate the TV's hotel mode menu. With the TV turned on, quickly press Mute, 1, 1, 9, Enter on the remote control. This will display the Hotel mode menu.
* With Hotel Mode option highlighted, press ENTER on the remote; press LEFT or RIGHT button to turn it on. Do not modify any of the other options.
* Press Power to turn off your TV.
* With the TV turned off, quickly press Info, Menu, Mute, Power on the remote. The TV will turn on and display the Service menu. If it doesn't, turn the TV off and try again. You need to press the buttons in succession VERY quickly.
From now on, it is important to follow the instructions exactly as listed here. DO NOT USE THE LEFT/RIGHT BUTTONS to scroll through options; you can only scroll through them with the UP/DOWN arrow. If you press the LEFT/RIGHT button by mistake, and you enter an option you don't want to change, press the RETURN button to go one step back.
* Scroll down to control (DOWN arrow), and press ENTER to enter that menu.
* Scroll down to Hotel Option, press ENTER;
* Remove any USB drives you may have attached. Scroll down to Clone TV to USB, and press ENTER. It says USB is not connected, which is fine. Press ENTER to close the message window. You are not actually going to do this, but this step is necessary to open up hidden options within the Sub Option menu.
* Press the BACK button to go one menu level up.
* Scroll up to Sub Option, and press ENTER.
* Scroll DOWN to Info Link Country. Press ENTER. Now press the LEFT or RIGHT arrow buttons to change to another country of your choice. Mine was set to None, and I switched to UK, which have the latest software. You may wish to try out others. Press the BACK button when you are ready to return to the menu.
* If your TV does not have PVR (TV recording) enabled, you can also enable it here!! Scroll DOWN (IMPORTANT: DO NOT USE LEFT/RIGHT ARROWS) to PVR Support, press ENTER, press LEFT or RIGHT arrow to enable it. Press BACK button to return to the menu. If you live in one of the few countries that can receive Gemstar (UK, Italy, etc), you may also enable Gemstar support two options down.
* When you are done, press the BACK button to move one menu level up, then scroll down to Hotel Option and press ENTER.
* Scroll to Hotel Mode (if it is not already highlighted), press ENTER to select it, and press LEFT or RIGHT to turn hotel mode off.
* Press Power to turn off your TV
That's it. Now the next time you enter Internet@TV, it will say it needs to update. It may delete a few services and install a few others specific for the country you have selected. It will also install the latest Internet@TV software update available on the selected country's server. Internet@TV may exit and restart.
The next time you enter Internet@TV, click on one of the problematic apps (Facebook, Youtube, Twitter or Picasa). It may still say new update found; turn TV off and back on. Don't panic. Turn TV off and back on, then enter Internet@TV again. It will perform a second update.
After all updates have been installed, you will have version 2.359 of the Internet@TV software, and Facebook, Twitter and so on will work!!
I hope you will find this walk-through useful.
(Mr Shaun Warburton may want to say something about this now, or maybe he still feels I don't deserve a reply!)
Finally, may I just say that all this hassle is because of inconsistencies across Samsung's servers, and Samsung failing to update their international servers with the latest software updates in a respectable amount of time.