I hardly ever use the Scope: Problems because I don't find any value in it (or I'm not understanding it/using it properly)
It seems like it could be equivalent to the eclipse problems view.
I find that feature good for two reasons:
Immediately shows where any errors are before you try to make/run/debug
Gives a sense of quality/latency of the project as it progresses (e.g. is the new code/changes adding more warnings)
I have a few issues with the current IDEA implentation
It just shows the files and doesn't break down to show the errors themselves
Files only seem to appear there once you have opened them, there is no background parsing of the project files on opening the project to populate this view