When you go back into a previously completed adventure to tackle a quest, it would be nice if each quest was explained in more detail, either through mouseover text or on the checklist itself. So, for instance, "No party deaths" might be explained further as "Complete this adventure without a single member of your party getting KO'd!" or something similar. Currently, the wording on each checklist item is not entirely clear. "No party deaths" could be interpreted as "no complete party wipes," for instance.
No party deaths could be renamed No one down or No Character deaths. Party death can sound ambigious, agree.