reading the firebug console in javascript

You could overwrite the console.log function to add whatever extra functionality you need.

var oldLog = console.log;
var lastLog;
console.log = function () {
    // do whatever you need to do here: store the logs into a different variable, etc
    // eg:
    lastLog = arguments;

    // then call the regular log command
    oldLog.apply(console, arguments);
};

This won't be the most bulletproof solution, since console allows printf style syntax:

console.log("%d + %d = %s", 1, 3, "four");

...but it's probably a start for you.

Don't try and override console.debug, implement a function that does console.debug plus what you need.

var debugCalls = [ ];
function myDebug(errorMessage){
  console.debug(errorMessage); //maintain original functionality
  debugCalls[debugCalls.length]  = errorMessage;
  //the previous argument to myDebug is debugCalls[debugCalls.length]

  //you may also want to call an ajax function to report this error
  mailError(errorMessage);
}

Could you rewrite the console.log(), and append all logs to an array? Then fire up the original console.log() and repeat what it's doing to get your debug output on the console?

Here's a more elaborate version I put together:

/**
 * Console log with memory
 *
 * Example:
 *
 *     console.log(1);
 *     console.history[0]; // [1]
 *
 *     console.log(123, 456);
 *     console.history.slice(-1)[0]; // [123, 456]
 *
 *     console.log('third');
 *     // Setting the limit immediately trims the array,
 *     // just like .length (but removes from start instead of end).
 *     console.history.limit = 2;
 *     console.history[0]; // [123, 456], the [1] has been removed
 *
 * @author Timo Tijhof, 2012
 */
console.log = (function () {
    var log  = console.log,
        limit = 10,
        history = [],
        slice = history.slice;

    function update() {
        if (history.length > limit) {
            // Trim the array leaving only the last N entries
            console.history.splice(0, console.history.length - limit);
        }
    }

    if (console.history !== undefined) {
        return log;
    }

    Object.defineProperty(history, 'limit', {
        get: function () { return limit; },
        set: function (val) {
            limit = val;
            update();
        }
    });

    console.history = history;

    return function () {
        history.push(slice.call(arguments));
        update();
        return log.apply(console, arguments);
    };

}());

You might wanna implement a queue. Expanding on Devin's answer: (something like this)

var window.log = [];

logger function(msg) {
  var log_length = 10;
  console.log(msg);
  window.log.push(msg);
  if(window.log.length > log_length) {
    window.log.shift()
  }
}

See:
How do you implement a Stack and a Queue in JavaScript?
http://aymanh.com/9-javascript-tips-you-may-not-know#string-concatenation-vs-arrayjoin