Is there a cost minimum for rental furnishing improvements; purchased furnishings in 2015 for 1/1/2016 in service vacation rental. Can I depreciate television $530?

The answer needs to address the fact that the item was purchased in 2015, before in service date.

See revised answer.

There is no minimum for improvements, as long as they are a permanent addition and increase the fair market value of your property.

Since this purchase was made before the property was ready and available to rent, the cost is added to the basis of the rental property, to be depreciated over 27.5 years. You may add this as a separate asset (NOT an improvement), or simply add the cost to the reported property basis.

When planning a project that spans multiple tax years, it's beneficial to wait until the property is listed before adding minor furnishings.

[revised]