An oscilloscope is always nice since it can not only show voltages, but also timing information.

But to verify that you can toggle all pins it is enough with a multimeter.

You write a test program that keeps the signals (one by one) in a static state - high or low. Then you will have all the time in the world to measure the voltage level of the pin with a multimeter.

This will make sure that you can toggle each and every output signal one at a time.

In the same way, you may externally drive every input signal one at a time, and have your program print out if the input pins are detected as high or low.

When you know that all processor pins works as expected, you can start trying to make full writes at a low speed by adding a nice and long delay between each display access.

With the above tests, you can figure out if you have an electrical problem, a logic problem adressing some pin or possibly a timing problem where you run a bit too fast for the display.

When trying to find a problem, the main goal shouldn't always be to find the error. It may be better to instead figure out what the error is not. The police spend most of their time by clearing suspects from their lists.