1. There should be a textbox allowing me to type a human-readable date/time (e.g. "monday 5pm" or "july 7, 2015").
2. The textbox should be selected and ready to type into as soon as the datepicker is opened
3. There should be a short list of previously-typed dates because often, for a given date in the UI, the same date is used multiple times in quick succession
4. There should be a typical month view with days of the week visible, in case I'm on mobile
5. The current date should be highlighted on the month view.
6. I should be able to pick the month and the year in at most two taps each (i.e. dropdown for each), no matter how far back in time I need to go.
Shameless plug: we recently implemented an exceptional date picker on momentcrm.com because of how frustrated we were with the default browser experience.