It is safe to burn diesel fuel in an oil furnace. Oil fuel is very similar to diesel fuel and the biggest difference is the color of the fuel. Diesel fuel also comes in more grades than oil fuel.
Over a long period of time, it can become expensive to burn diesel fuel unless it is of a significantly low grade. Burning diesel fuel does release a smell that some people find unpleasant, but these fumes are not dangerous. Diesel fuel is also not any more dangerous than oil fuel. It will not catch on fire or cause heat damage to homes.