Can DLC for the PC version of Dragon Age 2 be installed mid-game

The DLC is just scattered around the wasteland. In order to find the locations turn on your radio and you will see a bunch of new radio broadcasts. Listening to said broadcasts will make the DLC locations appear on your map (with the exception of Broken Steel). You can also go here and read the main article for each of the DLC's listed. The first quest in the main article has a "given by" section which will tell you how to access them:

As a side note when you reloaded the first disk after installing the dlc you should have gotten notifications that a new signal has appeared on your radio. So hopefully this isn't actually a bug.

The physical locations of the DLC (on your pc) are:

%USERPROFILE%\Local Settings\Application Data\Microsoft\Xlive\DLC (Windows XP)
%USERPROFILE%\AppData\Local\Microsoft\XLive\DLC (Windows Vista & Windows 7)

Just in case you want to check if they actually installed.

You should be able to do this in the console, with the command:

runscript zz_pre_debug

The description according to the Dragon age wiki is:

Starts the Prelude Debug Helper Script which allows modification of plot states and teleporting.

You access the console with the back tick character (`), although you can change it by doing the following:

Open the file "\BioWare\Dragon Age\Settings\KeyBindings.ini" in your My Documents folder. Find the line that says "OpenConsole_0". You can change the value after the equals sign (=) to the key or key combination you want to use for opening the console after running the game. E.g.: change it to "Keyboard::Button_Tilde" to open the console by pressing the ~ button in the top left corner of your keyboard.

Unfortunately, I am unable to find any information on how to use the script itself once you run it, and since I don't have the game on PC I can't test it out myself. Either way, I hope this helps.