I’m going to summarize/steal some of the ideas I’ve seen elsewhere and merge them with my own ideas.

I definitely like the simplicity of WorkFlowy’s approach. (This is why I found myself not using EverNote, but I always come back to WorkFlowy.) So I agree with other posters that a date/reminder system needs to be simple and stay out of the way of users who don’t want to use it.

I think that using the existing hashtag system is a good approach to build on for implementing dates and reminders. People could add the hashtags manually, or they could add the hashtags by clicking the bullet point next to their item and using dialogs similar to what Google Calendar or iCal use. The resulting hashtags could look similar to these:
 #Date:2016–05–05 #Date:2016–05–05[2:40PM]
 #RepeatingDate:WeeklyOnMonday[6:00PM] #RepeatingDate:MonthlyOnThe3rd #RepeatinDate:MonthlyFirstMonday #RepeatingDate:YearlyJune1st
 #Reminder:WeeklyOnMonday[6:00PM] #Reminder:2016–05–05[2:40PM]
 
Keeping dates and reminders separate is a good idea. Sometimes you want to set a date for something, but not want to be reminded of it, and vice versa. Reminders could take the form of email, or on-screen audio and/or visual notifications.
 
WorkFlowy should allow people to search for dated items or reminders using a GUI-type calendar or a manual text-based/hashtag search.

One of my biggest pet peeves with using WorkFlowy is that it is very hard to see all of my upcoming tasks without manually adding hashtags as part of an elaborate tracking system. Therefore, here is the most fundamental change that I would like to see that would make all of this worthwhile:
Allow users to toggle/permanently display an “Upcoming Tasks” pane at the top of their list. Allow users to view different versions of the Upcoming Tasks, such as “Right Now” (items that are due within, say, 4 hours), “Today” (all items due today), “Next 24 hours,” “Tomorrow,” “This Week,” “This Month,” and “All Upcoming Items.” Using the date’s users had set, this pane would show the upcoming tasks within the selected time frame. I know that this gets slightly away from WorkFlowy’s emphasis on simplicity, but it could be opt-in and the advantages would be enormous.

It would also be great if marking a task completed resulted in the addition of a similar hashtag that indicated when the task was completed, so you could go back and search by either when the task was due or when you completed it.