Let's start with the simple ones first..
This has been updated to include your watchlist, portfolio stocks or preset-searches. Previously it was only saved searches. You can configure that in the miscellaneous section of this page.
The search page now provides titles, if it can. The minute you resubmit it's lost because anything could have altered.
This is the biggest change. This has been vastly improved. When you choose to search by company name, or... when a search has run that is essentially a short-list, the search form will show something like the following:
Notice the familiar "look-up" widget.
Here you can add, or remove stocks from this list, and re-search them by clicking the "Short List" button.