How can I see and work with all of the filters applied on a report at once?
You can only do this in the DESIGN mode by making use of the Document Structure and Filters pane. (HTML mode used in this example.)
Document Structure and Filters tab allows you to view all the elements that make up the document, such as the reports, sections, report blocks, headers and footers, as well as the filters. You will need to expand the sections to see all of the filters and other details. (Numbers below refer to areas/actions seen in the screenshots.)