Before you jump straight to the comments section, yes I'm aware that Firefox 4 beta doesn't have to be compatible with pre-existing add-ons. The idea of my experiment was to see how much Firefox's new add-ons center changes the way browser extensions work. The answer is: a lot!
Hacking Firefox to make it run addons designed to run in previous versions of the browser is hardly an advanced job. Just add a couple of Boolean values to the advanced preferences and you can tell Minefield (the best name for a beta program ever!), not to check add-on compatibility. Generally, this can force compatibility when the version change is minor (e.g. 3.5 to 3.6). It doesn't usually work for most add-ons across major version updates.

And 4.0 is no exception! After telling Minefield (4.0b2Pre) to accept all my 3.6 add-ons and restarting, the extensions all appeared to have loaded satisfactorily. FoxyTunes, Alexa, Google Wave, Tumblr Post, Firebug and Echofon all appear in the status bar where I'd expect to see them. But none of them do anything. Nor does Greasemonkey. In fact, except for the built-in extensions, the only add-on currently seems to function is the classic Tab Mix Plus.
So for those of you asking the question: 'how do I force an add-on to be compatible with Firefox 4.0?', the answer is: You can't. Be patient, Firefox 4 will be released soon and your favorite add-ons will be updated in no time.

Farewell to Android
Klout is FarmVille for grown-ups
Does Flash matter on mobile?
What is Twitter?
Actually you can make add-ons compatible with Firefox 4.0 and any other version for that matter, nightly included. Just type about:config into the url bar and hit enter. Agree to the warning. then right click and select "new -> boolean -> extensions.checkCompatibility.4.0b -> false". If that doesn't work just swap out 4.0b for 3.7b. Then reboot your browser and choose which add-ons to install like you would normally. There are also add-ons for this job one is called "nightly tester tools". So far of all the add-ons I've tried only Xmarks and BetterPrivacy don't work right once compatibility check is disabled.
@Matt - have you tested this with 4.0 or one of the nightly builds? It doesn't work, so far as I can see... at least not with the add-ons mentioned in the post. Can you confirm that you've got it working?
I had a few addons that have continued to work, mainly AdBlock Plus and DownloadHelper (that's 2 of the main 4 I ever used). I can see most addons probably wouldn't work, but it's probably better to say they're 'not tested' or approved, as some do appear to work with no tinkering. :)
Yes using extensions.checkCompatibility.4.0b they still install not all will work like I said before. Now I'm assuming your talking about being able to install them from the add-on site itself, even if it shows the add-on as in compatible on the site, you can still click on it and it asks if you wish to install anyways? Just click on that button and eventually the same popup will show up as before and on the new Firefox 4.0 there is no popup once installed you have to click on the orange Firefox tab on the left then customization and then click on add-ons. It will then tell you their ready to be installed and to reboot And yes I just installed FoxyTunes on Firefox 4.0 beta 1. All Firefox 4.0 betas including nightlies will use the same code. All add-ons will install but not all will work. The reason some will work and some won't is because of how the new Firefox deals with add-ons it's not the same as before. Xmarks will go into a continuous syncing loop but won't fully sync and while BetterPrivacy will install I also get a message popup about something wrong. Just make sure you include extensions in the extensions.checkCompatibility.4.0b because it's one word and make sure you have no space before or after the extensions.checkCompatibility.4.0b or it won't work. But I just retested it to make sure and your FoxyTunes does install.
Here's a pic to show you it works http://i294.photobucket.com/albums/mm118/ViciouslyCold/Firefox40.png
I have an image of me having it installed but atm that post isn't showing up with the link. I can email to you if it doesn't ever show up here.
Well, Google Shortcuts 2.0.9 is already supported by Firefox 4.0b1 since its version 2.0.8. And its works fabulous... :) :) :)
@Matt - well I can produce the exact same screenshot as you, but none of the add-ons actually do anything. I see you've got Foxytunes installed. Can you make it control your music?
using 4.0b2 here and pretty much anything will install with the addon compatibility reporter installed but very very few of them work. Currently of the extensions I normally use the only ones I have working are firebug, adblock plus and linkification
Just tried this for Firefox 4.0b3 and it worked for (and I can completely vouch for) StumbleUpon and TabRenamer, though I did notice that my Firebug is not working. This was quite the good fix for the moment. Can't wait until the release so that 3rd party addons can be upgraded!
i am nowing getting back to 3.6
I tried the new Beta 4. I know how to type on the computer and that's about it. All the above advice is way beyond me. I found that it was not compatible with AVG, Malwaybytes, and something else. It told me that as it took the items off. I had no chance to say, "No" or "Cancel". I returned to the older version immediately. I have had crash after crash after crash. I did uninstall 4 before reinstalling the old version. I am not a happy camper. I can't even get more than one firefox window to open at a time, and after using for 3 to 4 hours it freezes and I have to reinstall again. I am dreading the release.
Hi nothing is working for me in the new 4.0 non beta in windows 7. I install some add-ons including the promo ones and it seems like they installed ok but they don't show up and I cant find them. It works great on XPbut that's because I refuse to do updates..trust issue...
Any ideas. Otherwise I have to go back to windows ie; I don't want to give them the satisfaction.
Yay!!! Found this site to downgrade back to Mozilla 3.6.16 as 4.0 just shows black screens and freezes about 5 minutes into program. http://www.aeinrst.info/downgrade-firefox-3-6-to-3-5-or-earlier-versions/
Step 1: Uninstall Firefox from your computer. Step 2: Download the version of Firefox that you would like to downgrade to from FileHippo Website. Step 3: Install the selected version and enjoy.
Here is our step by step guide to downgrading from Firefox 4 to Firefox 3: http://onsoftware.en.softonic.com/how-to-downgrade-to-firefox-3