Remove the possibility to share filter with everyone ?

In JIRA 5.1, this is possible to achieve by modifying the edit-share-types.jsp file, inside the JIRA-INSTALL/atlassian-jira/template/aui folder. You'll need to edit the file and modify from line 22-26, from:

<select id="share_type_selector">
                        <ww:iterator value=".">
                            <option value="<ww:property value="./shareType"/>"><ww:property value="./shareTypeLabel"/></option>
                        </ww:iterator>
                    </select>

To:

<select id="share_type_selector">
                        <ww:iterator value=".">
							<ww:if test="./shareTypeLabel != 'Everyone'">
                            <option value="<ww:property value="./shareType"/>"><ww:property value="./shareTypeLabel"/></option>
							</ww:if>
                        </ww:iterator>
                    </select>

Then, shutdown JIRA, delete the contents of the JIRA-INSTALL/work folder and restart JIRA (The contents of the work directory will be recreated during the restart).