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Show Javascript error count in Firefox without opening console

Now that Firebug has been subsumed into Firefox, how can I configure the browser to bring Javascript errors to my attention without having the console open all the time, as Firebug used to do by showing an error count on its toolbar icon?

The Firefox DevTools provide a so-called "Developer Toolbar" aka GCLI (openable via Firefox menu > Developer > Developer Toolbar or Shift + F2), which displays the number of errors on the page (besides providing many useful commands):
Update:
The DevTools team obviously plans to remove the Developer Toolbar, because of low usage and because it's unmaintained and for most of it's features are available somewhere else.
There is no replacement yet for the error count, though, but a comment on the related bug report indicates that it will be added back.

Another options is to use Chrome extension JavaScript Errors Notifier.
To install it in Firefox, you'll first have to install another extension Chrome Store Foxified, which enables you to install any Chrome extension from Chrome Web Store to Firefox. You can follow the instructions of Chrome Store Foxified to install the extensions you like. (Note that not all Chrome extensions will work in Firefox.)
If you want to install the Chrome extension permanently, you'll have to sign up with Mozilla to get the extension signed.
If the JavaScript Errors Notifier extension is successfully installed in Firefox, you'll see an icon appearing at the right end of the address bar.
And when there's any JavaScript error in the page, the icon will turn red. To see the details of the errors, you can click on the icon. And the extension have quite some options to tune the errors that you want to get alerted.

Unable to set breakpoint in chrome app

I seemed to have lost the ability to set a breakpoint in a chrome app. I tested with a chrome-app-sample and my old app in both canary and stable chrome with both chrome versions open simultaneously on a mac as well as only one open at a time.
Whether I try to set a breakpoint programmatically with debugger; or set the breakpoint in the sources tab of the Developer Tools app, I can not seem to stop on code that I am 100% confident is executed.
Version 41.0.2258.2 canary (64-bit)

cannot debug javascript from webstorm anymore

I used to be able to debug javascript from webstorm with no problem at all.
Thanks to the jetbrains chrome extension, it simply opened a new tab in chrome and launched my site in there with no problem whatsoever.
But recently I had to reboot my computer (with a beloved windows update) and now this is not working anymore.
When I start the debugging from webstorm chromes opens a new tab and I see the following in the address bar and then nothing...
data:text/html;base64,PCFET0NUWVBFIGh0bWw+PHRpdGxlPkxvYWRpbmcgaHR0cDovL3ZtLnNob3RndW4ubG9jYWwvPC90aXRsZT4=
My site is not opened and the page remains blank in chrome.

Most probably this is a result of Chrome update: some Chrome API changes introduced in v.37 break js debugger. WEB-12418 is fixed in WebStorm 9 EAP

Removing the Visual Studio / Visual Web Developer 2010 Express debugger and debugging JavaScript in the browser's debugger

When I set a break-point in my JavaScript code in the browser's debugger provided by its developer tools plug-in, I get a message saying that one or more processes are already attached to this, so it can't set a break-point or debug the code in the browser.
I know that if I run a deployed app, since it is not running in the Visual Studio environment, I can attach it to the browser's debugger.
But how do I debug an app already running in Debug mode inside Visual Studio / Visual Web Developer 2010 Express inside the browser?

You want to use IE developer tools script debugging.
Try this:
Goto:
Tools->Internet Options->Advanced->Under "Browsing"-> check both
options that starts with "Disable script debugging"
Open IE developer tools
(Press F12 or Tools-> "F12 Developer tools")
Enable script debugging
Open "script" tab and click button "start debugging"
If this works you will be able to debug your JS with IE developer tools.
Note: Why don't you use Chrome. It offers much better developer tools experience than IE.

How can I debug a Firefox extension with Firebug?

I'm trying to use Firebug to debug a JavaScript file in an extension I've added to Fx 4.
Can anyone tell me how to do it? I can only see website scripts.

Use Chromebug it's firebug for extension development, witch will give you the full ability to inspect debug firefox it self and all firefox extension as if it's a webpage :)
1- install the latest version from here: http://getfirebug.com/releases/chromebug/
2- Winkey+R to open run then type firefox.exe -chromebug this will run firefox with chromebug
3- for more information visit http://getfirebug.com/wiki/index.php/Chromebug

Please see MDN - Building An Extension - Debugging Extensions, which shows what tools Firefox provides you with to natively debug extension, also take a look at Dive Into Greasemonkey - Debugging User Scripts (PDF, p.13) which is aimed more specifically at your request.
Other than that, see How to debug a Greasemonkey script with the Firebug extension?

On Firefox 19 or later, it's possible to use the built-in JS debugger on the browser itself. Go to about:config and set the following two prefs:
devtools.chrome.enabled: true
devtools.debugger.remote-enabled: true
After you restart the browser, you can access the Browser Debugger through Tools > Web Developer > Browser Toolbox.
(note that you must accept the incoming connection)
See more at: https://developer.mozilla.org/en-US/docs/Mozilla/Debugging/Debugging_JavaScript#JavaScript_Debugger

In the bottom right hand corner there should be a little Firebug icon. Single or double click to open then you see some tabs at the top. Click the "Console" tab for real time debugging, or the "SCript" tab to view the scripts that have been loaded. Note, you can also load CSS and HTML through Firebug, use the "Viewer" icon to view HTML code on the page in real time.