Since I happen too have too much free time (NOT), I made a readable mockup.

It happens daily, and I'm wondering why I didn't take the time to make a feature request out of it.

My comment here would be

1. to precise the search scope:
No Match "in selection" (so you REALIZE clearly it's the wrong (smallest) scope, it happens).

2. Since it sounds counter-intuitive to make that no match dialog more than an ok box, what about just giving the focus in the scope field, where in 3 up or down key, I could move to document ?

Actual "after closing OK box state" is focus on "next" button, but still on selection (which won't match anything else, iD just told you)

Desired state would be a focus on the search field (see last picture).

I also run into this unexpected and undesirable behavior frequently.

Instead of just reporting "Cannot find match." I suggest the dialog box show the results but then be smart and offer the different search scopes as one-click buttons: Story, Document, All Documents.

That way the existing behavior is retained for whoever likes it, but functionality is added to quickly offer the options of what many users will naturally want after their initial search fails.

A little clarification of when this occurs in my work:
If I have a particular word or phrase--or any string of text--that I need to search for, I will often select and copy it so I can paste it into the "Find what:" field. ID automatically changes the "Search:" scope to "Selection," though this is almost NEVER what I want.
What it's doing is searching a selection for itself. If I realize that my client's name is misspelled on page 3 of a 500 page project, I'm going to want to make sure it's not misspelled anywhere else. To search for it, I'll select and copy "Amalgamated Coking Producks Incorporated" and paste it in the search window. I'll put "Amalgamated Cooking Products Incorporated" in the "Change to" field, and ID will search the selected text ("Amalgamated Coking Producks Incorporated") for "Amalgamated Coking Producks Incorporated."
Surprise! It will find it and replace it. Once.
Then it will tell me (with the annoying search completed message pop-up) that the search is completed. If I don't know that "Amalgamated Coking Producks Incorporated" exists twice (or 500 million times) in the document or story, I'll wrongly think I'm safe.
Whether I hit Change/Find or Change All, the result is that it's changed once and I'm told the search is completed.
I've been bothered by this for almost as long as I've used ID, which is as long as ID has existed, so I should know better, but it still gets me sometimes, forcing me to re-do searches, wasting my time and adding pointless clicks.
This behavior introduces massive potential for error into people's work and needs to be fixed.

This is one of the most annoying aspects of InDesign. If I'm searching the whole document (or the story), it finds what I'm looking for, I do something outside the search window, and some text is selected, then when I click back in the search window "document" or "story" changes to "selection." If I do another search, it won't find what I'm looking for because it's not in the selection. If I don't notice that it's searching only the selection, I'll wrongly think there's nothing to find.

I second that. Annoying to watch out for this.

Well, Tobias, I hope that there's a reason for this behaviour… :-)

Hm. I'm wondering, if this is a feature request or even better a bug report ...