If you run a cone search and then open a link to a separate query, the query executes the previous cone search too. Not sure how this is stored, but it's definitely not in the URL and only becomes apparent because you see no candidates.
I think this behaviour probably applies to the filtering (#3) even though it's not actually shown.
There are a few other silly things, like if you have Viewing set to a specific SBID, then the Observation filter does nothing.