Recovering a Differential Equation From the Transfer Function of a Cascaded System
You have discovered pole-zero cancellation, which is one of the reasons that state-space systems description was invented.  Another reason is because when you go from a differential equation to a transfer function, you lose information about the structure of a system that you can choose to preserve in a state-space description.

In general, you should be very careful when you see a pole-zero cancellation, because even if the pole is stable, it can still affect the behavior of the system on startup, if there is a transient that pushes the system into nonlinear behavior and excites the extra pole, or if the pole and the zero don't actually match up perfectly in the real world.

And yes, if you have an unstable pole that's cancelled by a zero then Bad Things will happen to the system that simply aren't described by the transfer function.