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Some of the new features that have been added to Open Office 3.1 are antialiased drawings to smooth the edges of graphics, replying to notes, improved grammar checking, hyperlink management and sorting, control of slideshow media, macro support for Open Office Base, relative database paths, better internationalization for Hebrew and Arabic plus performance improvements.
The full list of changes and new features can be seen in the official Open Office 3.1 documentation which lists all the major improvements over previous Open Office versions.