JQL needs something like:

now()=='Friday'

Use case:
As an Agile/Scrum/GreenHopper user we have an Agile project dashboard including a query for what we completed yesterday and what's assigned to us now.

This quick view is used extensively in the daily stand-up meetings where we normally present yesterdays work and current work.

This view fails us on Monday, as past day doesn't include friday or the occasional weekend work.

We can't use two queries because the dashboard views don't support such a thing.

We need a way for this query to work differently depending on the current day/time so that it can effectively be used in dashboard views.

Having a startOfDay(-1, 'BusinessDaysOnly') feature would be another solution to the problem.