To me it seems surprising, frightening, and sadly typical
Bombing the moon was mostly a "just because we can" demonstration of military superiority.
Using nuclear bombs on Mars is the only way we have of creating a planetwide effect without requiring an impossibly large amount of resources.
Would there be any flash?
From the article on the A119 proposed nuclear detonation on the Moon:
If the explosive device detonated on the surface, not in a lunar crater, the flash of explosive light would have been faintly visible to people on earth with their naked eye,
A surface detonation would not result in a mushroom, but there would be a 'cloud' of high-velocity debris.
On Mars, you would get a mushroom, although I suspect it'd be less visible than on Earth due to the lower atmospheric pressure, so less dust gets picked up. A quick search didn't turn up any studies on the effect of a large detonation on Mars.
There have been some reactions by scientists to Musk's plan, citing two major problems:
- it wouldn't be as quick as Musks hopes
- the fallout would be a major problem if you hope to make the planet habitable.