Unfortunately, you landlord is not obligated to replace a mercury thermostat as a general matter--mercury is an accepted substance for use in thermometers and thermostats. It is possible that under your state or even local city/municipality rules, mercury thermostats may be barred; the easiest way to check is to contact your local building department. If there is any code requiring its replacement, that should be enforceable; but otherwise, as noted above, the fact that it's mercury would not require replacement.If the thermostat is so broken or defective that it prevents the heat (or central air, if any) from working properly in your rental, that might require the landlord to replace it (though he could possibly replace it with a new mercury-based one), since a failure of the heating system could violate the implied warranty of habitabiltiy. But if the heat still works, then this would not apply.