Firstly, the short and simple answer is because they don't. Part of that is that movies don't bother with the frills, if the frills get in the way of elegant storytelling.
This is no different from why people don't say hi/bye during phone calls, or why scenes don't get interrupted by people taking bathroom breaks. It would be more realistic, but it doesn't matter to the plot so incorporating it into the story provides no benefit.
Secondly, the hospital is in the middle of an evacuation due to a bomb threat. The corridor you see the nurse (later revealed to be the Joker) walk though is filled with people either panicking or frantically running around trying to evacuate themselves or others.
It's perfectly reasonably for those people to not notice Joker.
The same logic applies to the actual evacuation post-explosion. In that scenario, people are looking for anyone who isn't there who is supposed to be (i.e. people who didn't evacuate), they're not focusing on people who are there who aren't supposed to be.
Thirdly, there's the consideration of what would happen even if they noticed him. Are civilians really going to interfere with what amounts to a grotesque domestic terrorist, if he is currently not actually threatening them?
Similar to the first point I made, if civilians spotting the Joker makes no difference to the plot, then it's an unnecessary scene that can easily be omitted in an otherwise already eventful and long movie.