Is corrosion on top to an otherwise working electric water heater dangerous?
No matter what, it won't explode. Maybe a little bit of splat. But no boom. Ok, really, more of a squishing sound, the sound of your feet splashing through the puddle created when it fails. :)

There may well be an anode, connected to the input line. Or at least there was one, probably corroded away now.

Assuming a little water on the floor won't hurt anything, I would buy an inexpensive alarm that senses the presence of water on the floor. Its just a pair of contacts that set off a battery powered alarm when water bridges the gap. When it goes off, buy a new heater.

If some water in that area will be a problem, then the heater should be in a low pan that will catch a leak. If not, then consider a preemptive replacement, as this heater probably has only a few more years in it anyway.