My ride on briggs and stratton just stopped. It had been blowing whitish grey smoke, especially just after reversing or changing speed. I did leave the lid of the oil loose last time and oil spattered everywhere. It has enough oil in it.

Whitish gray smoke leads me to think your head gasket may have blown. Do you know how to measure the cylinder compression? This would help to confirm or deny the blown gasket.

With a loose dip stick you will loose crankcase vacume and push oil out the breather. Oil will spill on muffler and vaporize the vapor will be drawn into carb and can kill engine.

Head gasket would surprise me but I have been wrong before.. . 1962?

Has enough oil in it? Make sure its not overfilled... and dipstick tube and the upper seal on it are sealing tightly.