Ok, so you are seeing something different than I was originally seeing.
My applets originally wouldn't load at all (due to the libnss exception I mentioned above) ... you are saying that your applet would load but just not work properly.

I don't have an account that I can use to log into the Canada Revenue Agency's site.  However, when I run firefox from a terminal and go to the link you mentioned above (https://blrscr3.egs-seg.gc.ca/gol-ged/gov/browserdetection/BrowserCheck.html), I do see a bunch of output in the console:

java version "1.6.0_20"
OpenJDK Runtime Environment (IcedTea6 1.9pre) (6b20~pre1-0ubuntu2)
OpenJDK 64-Bit Server VM (build 17.0-b16, mixed mode)
[EntrustTruePassApplet/8.0 SP2] [DEBUG] CharacterEncoding=UTF8
[EntrustTruePassApplet/8.0 SP2] [DEBUG] LargeFileUploadChunkSize=8192
[EntrustTruePassApplet/8.0 SP2] [DEBUG] ForceKeyUpdate=0
[EntrustTruePassApplet/8.0 SP2] [DEBUG] KeyRolloverPercentage=42
[EntrustTruePassApplet/8.0 SP2] [DEBUG] PreserveClientApiFrame=ON
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ProxyTransactionBadInputWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ChangePasswordHistoryErrorWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Initialized
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Roaming EPF applet started
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Stopped
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Destroyed
[EntrustTruePassApplet/8.0 SP2] [DEBUG] CharacterEncoding=UTF8
[EntrustTruePassApplet/8.0 SP2] [DEBUG] LargeFileUploadChunkSize=8192
[EntrustTruePassApplet/8.0 SP2] [DEBUG] ForceKeyUpdate=0
[EntrustTruePassApplet/8.0 SP2] [DEBUG] KeyRolloverPercentage=42
[EntrustTruePassApplet/8.0 SP2] [DEBUG] PreserveClientApiFrame=ON
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ProxyTransactionBadInputWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ChangePasswordHistoryErrorWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Initialized
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Roaming EPF applet started
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Stopped
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Destroyed
[EntrustProfileApplet/8.0 SP1] [INFORMATIONAL] Initialized
[EntrustProfileApplet/8.0 SP1] [INFORMATIONAL] Roaming EPF applet started
[EntrustProfileApplet/8.0 SP1] [INFORMATIONAL] Stopped
[EntrustProfileApplet/8.0 SP1] [INFORMATIONAL] Destroyed
[EntrustTruePassApplet/8.0 SP2] [DEBUG] CharacterEncoding=UTF8
[EntrustTruePassApplet/8.0 SP2] [DEBUG] LargeFileUploadChunkSize=8192
[EntrustTruePassApplet/8.0 SP2] [DEBUG] ForceKeyUpdate=0
[EntrustTruePassApplet/8.0 SP2] [DEBUG] KeyRolloverPercentage=42
[EntrustTruePassApplet/8.0 SP2] [DEBUG] PreserveClientApiFrame=ON
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ProxyTransactionBadInputWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [WARNING] Applet parameter ChangePasswordHistoryErrorWebPageUrl has not been set.
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Initialized
[EntrustTruePassApplet/8.0 SP2] [INFORMATIONAL] Roaming EPF applet started

You should try running firefox from the console again and go through whatever steps are not working, and see if anything useful is printed on the console.