IE7 will ship this year and offer features that bring it in many ways to feature parity with Firefox. It also more prominently exposes several features, like RSS, phishing filter, etc.
Advance the state of the art of browsing, while improving on Firefox's simplicity and ease of use.
Some issues with Firefox's browser window:
Tie together similar functions in the browser window. Make usefully clickable items appear clickable. Remove or hide by default items that aren't as often used.
Update the visual design, while making sure that the application still looks at home on each of its target platforms, and adheres as closely as possible to user preferences within the operating system.
Group the back and forward buttons into a single unit. Use research to determine a better method for multi-page "chapter stop" navigation than offered by the not-often-discovered-or-used dropdown menus.
The location bar cluster should contain all status indicators and commands specific to the current location loaded. It might consist of a site icon, the site's URL, static or semi-static indicators relating to information about the page whose presence imparts important information, and a set of buttons that offer commands that can be performed on the URL in the text box: subscribe, add bookmark, reload, stop, go.
Buttons for History and Home can start the Bookmarks toolbar, since they are thematically related.
By showing important information about loading progress in the location bar, the status bar can be simplified and hidden by default. The window resize gripper can be overlaid over the content area. Windows opened without chrome will have a single strip at the top forced that contains a read-only location bar showing the user the URL, the security and phishing state.
If possible, the back button should have more visual prominence than the forward button.
Command buttons associated with functions operating on the displayed URL should appear visually connected to the location bar. They need not appear inside the "sunken" tray that is the edit box, but should flow into its shape, not be bigger or smaller. They should have a button-like 3D appearance.
This is similar to Safari's SnapBack feature, except more usefully exposed. Either place a button between the Back and Forward buttons, or offer an additional menu item inside the session history drop down that shows the chapter mark, if it is not displayed in the list of the most recent 10 pages. The latter approach is useful if the "mystery button" behavior of SnapBack proves undesirable, the former is desirable because it does rely on the user discovering the drop down menu. Either approach is preferable to the Safari approach that places the button in a less visible part of the screen (the location bar) well away from the primary renavigation cluster.
A "New Tab" button with dropmarker on the tab strip. The default action is to create a new tab. The drop down menu exposes additional commands, similar to the context menu. The user should be able to use this menu to open a tab they already closed. This might be done by showing a list of recently closed tabs, or just the last one. Many propose "Undo Close Tab" but undo does not seem to be a logical action for closing a window.
...
Make it easy for people to keep track of their favorite pages and subscribe to updates to their content. The browser should offer a quick way to save a link for future use without any cumbersome management overhead. The browser should also detect pages syndicating their content using various syndication technologies and dispatch to the appropriate application.