Aha! I am using Safari and the Safari user agent styles seem to push the year-picker out of view. I see it now, in the source.
On line 332 of style.date_picker.css add “display: inline-block” and both selects are shown!
.ui-acf .ui-datepicker select.ui-datepicker-month,
.ui-acf .ui-datepicker select.ui-datepicker-year {
width: 47%;
padding: 1px;
font-size: 12px;
font-weight: normal;
display: inline-block;
}