Doesn't pin 10 need to be connected to the + supply powering the motor? Especially with inductive loads like motors, solenoids, etc. it's important to have that diode in-circuit, otherwise any back EMF would flow through the parasitic internal diodes and probably fry the chip eventually.
Speaking from personal experience, you MUST have limiting resistors while driving anything that is related to LEDs. I have twice ignored limiting resistors for my 8x8 dot matrix and both the times, in the long run, I have burnt more than one of the LEDs making the entire matrix useless. I was using RasPi to control the matrix. Resistors are extra redundancies that you should have to prevent your hardware from any damage in the long run.
