Internet Explorer is particularly buggy as reported by users especially with editing text. This is an unfortunate limitation of this browser.
As noted here: http://support.gliffy.com/entries/21406275-Browser-Minimum-Requirements-for-Gliffy-HTML5, we recommend using Chrome or Firefox for the best user experience.
If you are required to use Internet Explorer and double-clicking to edit text is not working for you, you will want to click once and hit F2 on on your keyboard.
If you have further questions or difficulties, please contact us at firstname.lastname@example.org. Thanks!