How can I tell when Finder is done searching? I don't see any progress indicator, and the title of the window says:

Searching "[Directory]"


Is there supposed to be something that happens to let me know when the search is complete?  On some large directories (tens of thousands of files in hundreds of sub-directories) I know the search isn't complete, because it hasn't found files that I know are there, and I usually give up before it finds them.  So on a directory with less files it is rather concerning to see no indication if the search is done yet or not, especially when nothing has been found that I hope will be found, but am not sure if will.
Yes you can. Turn on the status bar: View > Show Status Bar.

There you can see whether the Mac is searching.