I uncovered the cause of this in my own question.

The console injects its own function (just a shorthand) for document.getElementById(), aliased to $, which shadows jQuery's $. Easy way to check this: when you're at a breakpoint, and jQuery seems to be broken, compare the following in the console:

• jQuery
• $
• window.$

The first and last will be jQuery proper, the local $ is something like:

function () {
    return document.getElementById.apply(document, arguments)
}

This is because code run from the console is wrapped in a with statement:

with (window ? window.console._commandLineApi : {}) {
with (window) {
    // the actual code you typed in here
}   
}

and window._commandLineApi.$ is the function that shadows jQuery.

Found the bug in Chromium for this: http://code.google.com/p/chromium/issues/detail?id=70969

Just run the following command on the console to make it work:

$ = jQuery