When I first publish an entry, leaving the entry date at the default current value and setting an expiration date, the datepicker works fine.
If I then go back and immediately edit that entry, there are problems:

In Chrome, I just get the datepicker pop-up with an undefined NaN heading and no dates for both the entry and expiration date.
In Firefox, the datepicker loads fine but shows a completely different date e.g.
20/6/2016 14:58 in the entry date field but the datepicker shows 6 August 2017
26/6/2016 23:48 in the expiration date field but the datepicker shows 6 February 2018

While this issue seems to happen consistently for brand new entries edited at the moment, it’s less predictable for older existing entries.
In Chrome, the entry date datepicker still tends to show undefined NaN while the expiration date datepicker tends to load OK.
In Firefox the date shown in the datepicker makes sense for older entries unlike the weird dates for just published entries as per above example.

However, in both browsers, the datepicker usually shows the wrong format date i.e. my field has date entered in d/m/y format but the datepicker shows it in m/d/y format, even though my time zone is set to Ireland with dd/mm/yyyy as the format in system settings (with my account set to use the site default).
For example,  if my date field is set to 5/7/2016 23:55 (5 July) the datepicker will show 7 May.