What people need to understand about LMDE is that Firefox and Thunderbird for Debian and thus LMDE are now packaged and updated by Clem and Co and have been for awhile now (. Why this hasn't been done for Firefox 4.0 and the latest Thunderbird lately I haven't a clue but I would surmise it may be be due to the work that needs to be put into LM 11 (main edition) which has taken a significant turn away from the stock Ubuntu base (Using Gnome 3 without gnome-shell instead of Gnome 2.32 with Unity). That plus "ikey" having to leave Mint due to personal reasons has probably slowed development right down.
I'd go find the reference to Firefox and Thunderbird for Debian and thus LMDE being packaged now by Mint but it seems that everything but the Mint forums are down for the count including the repos. So here's an early reference from the Crunchbang Staler forums:http://crunchbanglinux.org/forums/topic ... n-statler/
Until things get straightened out I suggest using the Foxtester add-on for Firefox that allows you to install and run as many versions of Firefox side by side as you wish. It also allows you to set one of them as the system default. It's made for Ubuntu users but works fine on LMDE although you may have to change the menu path entries Firefox manually after you set a newer version as default. Works a treat for me.
Foxtester (latest): http://www.webgapps.org/addons/foxtester
Just make sure you follow the instructions. It's fairly easy though.
"Humph. Choice, it is the quintessential Linux delusion, simultaneously the source of it's greatest strength, and it's greatest weakness." (All apologies to The Architect)