I would love to have this. One of the members of my work group never adds due times so the reminder notification only plays if you have a notification set for all tasks due that day. It does not play when that specific task is due.

I would like to be able to occasionally search for tasks without a due time but with a due date so that I can easily find the tasks missing this bit of information and assign due times. (and the analyst I could use to automate this search)

I'm not sure why folks are voting against this feature rather than abstaining but this would be a mighty helpful search option.

I agree. I probably wouldn't use this a lot but it would be an additional feature to make RTM more flexible and powerful. If you don't use, it wouldn't get in the way of how you use RTM so it's a good idea even if you don't use it.

It sounds good to me.

I was needing this recently.

It's a tad complicated but there is a way you can search for tasks due today but with no due time. See this tips and tricks blog post:

http://blog.rememberthemilk.com/2013/10/tips-tricks-tuesday-separating-timed-and-untimed-tasks-with-smart-lists/