What is the Danger in Plugging an 4 Ohm Speaker into an 8 Ohm Amplifier?
The only real "danger" is that you won't be able to get the full rated power out of the amplifier before it starts to distort.

The power supplies and output stage are designed to deliver current in a certain proportion to voltage, with the proportionality constant being the load impedance.

If you put a lower impedance on the output (e.g., 4&Omega;), it will reach its current limit before it reaches its voltage limit. The sound will be undistorted up to that point, but will be clipped above it.

If you put a higher impedance on it (e.g., 16&Omega;), it will reach its voltage limit before it maxes out on current.

Either way, you'll only get about half the rated power.