( EDIT: My love of revsets made me ignore the obvious answer: hg update --date 2012-04-04 should get the latest revision from this date.)
If you have already cloned the entire repository (date specifications do not work with clone ), you can do
hg update --rev "date('< 2012-04-04')"
If there is a possibility that there were several goals / branches in the repository at the right date, you will need to narrow it down to the desired set of changes in some additional conditions:
hg update --rev "date('< 2012-04-04') and branch(v1.1)"
See hg help revsets and hg help dates more details.
Later, if you want to go back to the tip, just
hg update
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