This is a good start. This review is mostly about backbone fundamentals and some high-level coding style.
Once you do a little cleanup here, I'd like to see you prototype out the backend with models and API.

A note on indentation:

- Python is 4 spaces

- Javascript is also 4 spaces

- CSS should be 2 spaces

- HTML should be one (with the added complication that we do funky things re: django template tags)

This should be split up:

tagName: 'li',
className: 'item',

There should be a space between the argument list () and the {

This can be simplified and cleaned up a lot by using underscore templates. Something like this:

template: _.template([
    '<% if (finished) { %><strike><% } %>',
    '<a class="itemDone" href="#"><%- description %></a>',
    '<% if (finished) { %></strike><% } %>',
    '<a class="delItem" href="#">(X)</a>'
].join('')),

render: function() {
    this.$el.html(this.template(this.model.attributes));
    return this;
},

Leftover debug output?

Comments should have spaces between the comment markers and the text. Since these are all one-line, you could change them to //, too.

Space between comment marker and text. Please also capitalize sentences.

Backbone views have a this.$el attribute which is already wrapped in jquery. This can probably use .html with a single string--that way it reduces the number of calls that manipulate the DOM, and using .html means render can be called idempotently.
You might also want to save the ul element to an attribute, like this:

this._$ul = this.$('ul');


which would let you do this in appendItem:

this._$ul.append(checklistItemView.render().el);

Multi-line comments should use / /

jquery, underscore and backbone should all be available on all pages in review board. You shouldn't ship them as part of your extension and you shouldn't need to explicitly load any of them.

Hey Elaine,
Just took a pass at this, and have a few comments. See below!
-Mike

We probably want checkboxes to toggle these.

Can probably be replaced with X icons.

This can probably be replaced with a simple + icon.

How will this checklist go away if I don't need to refer to it?

A general nit that we should be using 4 space indentation throughout your JS files.

We prefer href="#" over javascript:void(0);, since it degrades somewhat more gracefully.

We could probably replace this with an icon, no?

I think itemID is too generic - we might want to make them more specific to checklists - so checklistItemID or something.

Again, href="#". Also, the indentation should be fixed here.

I don't believe we need all of this boilerplate in your template since it should already be all available in the places where you want your view.

Might as well make this a one-liner, like:
<div id="checklist"></div>

Is myChecklist ever going to be used? If not, why do we need it?

The checklist should probably be a floaty thing on top of the page, and not in its own scrollable view taking space away from the diff viewer.

Two blank lines.

Spaces inside the / and /

Space before {
Same below.

Margins, paddings, with, right, top, etc. do not use percents. They should be integers.

You're sharing a global ID space. You should always have a checklist_ prefix for IDs.

Same with classes. .checklist-item

CSS classes aren't camelCase. This should be .checklist-del-item

Trailing blank line.

Needs to be 4 spaces. Please go through the rest of the code (and your editor) and make sure 4 space indentation is used only.
What's this file for, btw?

Some browsers will break with trailing commas. Make sure you don't have any.

No need for the _(this.collection.models). You can just use this.collection.models.each(...)
Make sure to have a space before {.

Variable declarations must always be at the top of the function.

Same here with variables.
Also, only one var statement, like:
var id = ...,
    item = ...;

Two blank lines.

Python and JavaScript code should always use 4 space indentation, no tabs.

This isn't needed with the new static media setup.

It's not terribly important given that this is WIP, but for future reference, python imports are broken up into 3 sections:
standard library
other 3rd party
this module.

We also alphabetize these. You should also avoid from ... import *, because it can cause weird namespacing problems. You don't use any standard library stuff, so you'd have something like this:

from django.contrib.auth.models import User
from django.http import HttpResponse
from django.shortcuts import render_to_response
from djblets.webapi.decorators import (webapi_login_required,
                                       webapi_request_fields,
                                       webapi_response_errors)
from djblets.webapi.resources import WebAPIResource
from reviewboard.reviews.models import ReviewRequest
from reviewboard.webapi.base import WebAPIResponse

from checklist.models import Checklist

This should be Checklist without quotes.

If you correctly define "model" above, you should actually be able to skip defining this.

You should add user_id and review_request_id in a @webapi_request_fields decorator.

This should defined @webapi_request_fields with anything that you pull out of kwargs.

All django models automatically get a field called 'id' which is an auto-incrementing primary key. You don't need this.

This should probably be called "review_request"

Python code typically separates words with underscores (except in class names, which use CamelCase), so these should be items_counter, checklist_items, add_item, etc.

This should probably be called "toggle" instead of "edit", since it doesn't accept a new value.

This should look something like this, so that url() will resolve properly for both existing and new checklist items:

var baseURL = '/api/extensions/checklist.extension.Checklist/checklists/';

return this.isNew() ? baseURL : (baseURL + this.id + '/');