Question: Will this work with other browsers?

The short answer:
Chrome - most likely, with TamperMonkey extension or emulator script
Safari - maybe, with GreaseKit/SIMBL
IE - no, some features may partially work with Trixie addon
Opera - most likely, with an emulator script
Others - no or partially, without an extra program/addon

The long answer:
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Most browsers either natively support user scripts or have some sort of addon that supports it. The main problem is getting Greasemonkey-specific functions (specifically XPath, GM_xmlhttpRequest, GM_setValue, GM_getValue, and later on, maybe GM_log) to work which are used for comment autosave functionality, retrieving the NetID, and in the future, retrieving other information. Luckily, there are Greasemonkey-type addons that fully or partially support this. And further testing will verify if these work well.

* Chrome - I used an earlier version of the script on an old version of Chrome (without any GM-type addons) at home. The install was really easy - clicking the link would make a popup appear asking if you want it installed. However, the links were only displayed after refreshing the page. I installed a later version of the script, and it didn't work at all. 

There are extensions on Chrome like TamperMonkey (https://chrome.google.com/webstore/detail/dhdgffkkebhmkfjojejmpbldmpobfkfo) and TamperMonkey Beta (https://chrome.google.com/webstore/detail/gcalenpjmijncebpfijmoaglllgpjagf) that claim they allow this functionality. An emulator script (http://userscripts.org/scripts/show/68559) is another option. I have not tested these yet but based on their feature list, it is highly likely that they would work.

* Safari - I found an addon for Safari called GreaseKit (http://8-p.info/greasekit/). It says it supports the GM-specific functions in the HDRT script. GreaseKit requires an application enhancement program for Mac OS X called SIMBL (http://www.culater.net/software/SIMBL/SIMBL.php). This looks like it would work, but I don't have a Mac at home, so if someone could try this and see if there are any bugs, that would be nice. I'll try to test it at HD/RN, but I would rather prioritize finishing the inline comment box, adding other features, and testing it on Chrome. Also Macs have Firefox and Chrome.

* IE - Trixie (http://www.bhelpuri.net/Trixie/) claims it has partial support for GM functionality (specifically partial GM_xmlhttpRequest which may be good enough to retrieve the NetID). This will probably not work well. There's also an addon called IE7Pro. However, the way it implements GM-style functionality is different than GM, so it would be hard to maintain a parallel script for IE7Pro. I may try to test Trixie at RN, after adding some more features and testing on Chrome/Safari. However, Windows has Firefox and Chrome available, and I don't think IE is used to access HDRT often. The combination of poor GM support from Trixie, availability of other browsers, and lack of IE use makes testing on IE a low priority.

* Opera - Opera handles GM scripts in a special way (http://www.opera.com/docs/userjs/examples/). For GM-specific functions, there is a script written by an Opera employee that claims to emulate these in Opera (http://www.howtocreate.co.uk/operaStuff/userJavaScript.html#compatibility | direct link - http://www.howtocreate.co.uk/operaStuff/userjs/aagmfunctions.js). I have not tested Opera with or without the emulator script, and I'm not sure if it's worth it to test, because I don't think many HD consultants use it. I think the emulator script will work fairly well though, and it doesn't require installing any extra programs.
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