The edge should be quite sharp. Any deformation or movement in the edge will be smoothed extremely quickly, on timescales comparable to the light-crossing time of the object -- in this case ten seconds or so.
If you're a photon and you're in, you stay in. If you're out and heading out, you get out. (if you skim the surface, you might make an orbit and then leave :) ). It is that fact that makes the edge quite sharp.
I disagree. The edge of a BH is essentially an asymptote. While there is a mathematical bright line, when looking at it you should see light in all manner of red/blue-shifted colors near the event horizon. Since that light is coming in from a variety of directions it leaves in a variety of directions too. Everything would look soft and fuzzy around the edges. Out of focus.
Out of focus? I don't know about you but I find the black hole "edge" in the simulated images in Interstellar quite sharp.
(Or are you talking about resolving matter/light near the event horizon? In that case I agree – one won't really resolve any structures anymore due to light getting bent and redshifted in a myriad of ways.)
In case you weren't being rhetorical, the sun's edge would either be the chromosphere[0] or the corona[1], the corona being famously fuzzy and also quite bafflingly hot. The chromosphere is "smoother", but still very interesting on any given day [2].
this is sort of getting into the definition of black holes and event horizons. I don't think they really have solid surfaces, I would expect all imaging here to show fuzzy samples.
I couldn't really say for sure but I think macroscopically (viewed from a low-resolution telescope) it would look fuzzy, but close up, it would look very spiky and dynamic with all sorts of stochastic events happening.
If you're a photon and you're in, you stay in. If you're out and heading out, you get out. (if you skim the surface, you might make an orbit and then leave :) ). It is that fact that makes the edge quite sharp.