Is there a law that states how often a landlord is REQUIRED to put in new carpeting?I live in Michigan if that makes a difference at all. ...

There may be a specific law in Michigan that requires as
much; but I seriously doubt it. As a general rule, the Landlord has no obligation to the
tenant other than to ensure his quiet enjoyment of the premises, not misrepresent the
condition of the premises, and ensure that they be kept reasonably safe. Repairs, etc.
are often matters of negotiation between landlord and tenant and are usually written
into the terms of the lease. It is to the Landlord's advantage to keep the premises in
good repair as it makes it easier for him to rent the premises and receive a reasonable
return on his investment. Contrary to what you may have heard, tenants normally have an
obligation to return the premises to the Landlord at the end of the lease in the same
condition they received it, reasonable wear and tear excepted. If the last tenant left
the premises in good order, subject to reasonable wear and tear on the carpet, the
landlord is under no obligation other than not to misrepresent the condition of the
premises.