LiveJournal uses Unicode to store and display everything: text of journal entries, comments, names and personal information... everything. Unicode is a very powerful standard for working with text. For example, it allows users to store and input information in many languages at once. It supports the infrastructure of translating and maintaining the user interface in languages other than English.
Journal entries and comments which had been stored before LiveJournal switched to Unicode need to be converted to Unicode on-the-fly in order for the user to be able to view or edit them. This page explains how to deal with some of the common problems in that area.
Short answer: (applicable if you write your journal in English): Go to the Change Settings page. Choose "Western European (Windows)" from the pull-down menu and save your settings. Your entries should now be editable.
Long answer: In order to allow you to edit a non-Unicode entry, LiveJournal code needs to know which encoding that entry has been posted in. For users of English and other West European languages, this will normally be "Western European (Windows)", although if that doesn't work well for quote characters and other similar meta-characters, try "Western European (ISO)". Users writing in other languages should select their encoding; if it isn't in the supplied list, contact Support and explain the problem.
Note that "non-Unicode entry" may mean either a journal entry posted before LiveJournal underwent the conversion to Unicode, or a new journal entry posted recently with a client program that is not Unicode-compatible.
If there is a newer version of your client program that supports Unicode, upgrade. If not, you will be able to edit entries which contain ASCII symbols only (basically the Latin alphabet and the usual punctuation signs). For entries any fancy symbols or other languages you will have to resort to editing via the web interface, which works fine in any case.
This is probably due to you having friend groups with names that aren't exclusively ASCII (for example, written in non-Latin languages or containing accent symbols). In order to successfully work with such group names, you have to use a Unicode-supporting client. Alternatively, you can rename your groups to ASCII-only names on the group editing page and then use your client program.
You can try asking your question in the Support Area.