Elevators are very expensive to repair and/or replace. Most landlords would rather use a duct tape and bubblegum approach than spend the dough to do the job correctly.
If you are using the fireplace correctly and smoke is still billowing into your apartment, then it looks like a chimney cleaning is in order.
Do you rent the unit, despite it’s relatively minor problems, or do you point them out to your prospective landlord and risk losing an opportunity to rent a reasonably priced apartment?
You can always ask the landlord for his permission to paint or upgrade the carpet yourself. I rarely recommend that a tenant upgrade a landlord’s property, but small fixes and new paint may be justifiable because the benefits may justify the cost.
Tenants: You have to remember that you don’t own your unit. Rarely is it worthwhile to improve a property you don’t own. It never makes sense to improve a rental unit without the landlord’s written permission.