When using the search functionality in the inspector, we show a little yellow bubble ala Safari's Find in Page UI. There's no way to get rid of it though and clearing the search field deselects the document you're looking at. Would be nice if there were some way to get rid of it once you've found what you're looking for.
Need some clarification: what do you mean by "clearing the search field deselects the document you are looking at"? Does the "Esc" key work better in your case?
I can see no issues with this use case on ToT, the elements tree gets focused when the search is canceled.