Holy cow, I wrote a book!
The nickname for the feature known as
Windows Error Reporting is "Dr. Watson".
Where did that name come from?
As you have probably guessed,
The name Dr. Watson was inspired by
the character of Dr. Watson,
the assistant to
Sherlock Holmes in the stories
by Arthur Conan Doyle.
It is my understanding that the doctor
was originally developed as part of Windows 3.0 beta testing.
His job was to record data about application crashes to a file,
so that the file could be uploaded and included with bug reports.
The icon was (and continues to be) a friendly doctor using
his stethoscope to investigate a problem.
The Doctor has remained true to the
"capture information about an error" aspect of his job.
In the meantime, the word "Watson" has expanded its meaning
anonymous end-user feedback mechanisms in general,
such as "Content Watson".
(But if you hear "Watson" by itself,
the speaker is almost certainly talking about error reporting.)