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One can currently save the contents of a shell window exactly as is, with opening message, prompts, and restarts. This essentially a screenshot of the frame -- fine for an IDLE doc but not useful for rerunning the code.
Similarly, if one pastes in interactive input/output, with or without secondary prompts, into an edit window, it is a nuisance to edit.
This issue proposes an option to 'flip' code and output lines, with prompts deleted and outputs commented, so that
Python 3.2 (r32:88445, Feb 20 2011, 21:29:02) [MSC v.1500 32 bit (Intel)] on win32
Type "copyright", "credits" or "license()" for more information.
>>> 1+2
3
becomes
#Python 3.2 (r32:88445, Feb 20 2011, 21:29:02) [MSC v.1500 32 bit (Intel)] on win32
#Type "copyright", "credits" or "license()" for more information.
1+2
#3
(Ignore linewrap artifact on first line).

Roger Serway pointed me to the PastePyShell.py extension that is part of the IdleX package http://idlex.sourceforge.net/ 
That does the conversion when *pasting* interpreter text into an edit window. I would have File/Save do the same thing when saving the shell text to a .py file.

I considered saving directly from the shell but then I ran into a use-case problem. Saving the shell window as an runnable script will also save any syntax errors that were entered. A user would then have to open an editor to correct these errors.
A high-level task analysis would be as follows:
With "Save As Runnable", the user needs to save, open, and then fix.
With "Paste from Shell", the user needs to copy, paste, and then fix.
If you have suggestions for handling shell errors, I'm open to them.

Either way, it would be nice to have erroneous commands flagged or filtered. That can be detected when the first line of output is 
Traceback (most recent call last):
I typically would copy, correct, and rerun a line until I get it correct, so I would want bad lines just removed. Others might prefer otherwise. I should take a look at your extension when I get a chance.

This issue relates to #1178
A traceback does not necessarily mean that the last statement had the error. For example:
 >>> a = lambda: 1/0
 >>> a()
 Traceback (most recent call last):
 File "<pyshell#1>", line 1, in <module>
 a()
 File "<pyshell#0>", line 1, in <lambda>
 a = lambda: 1/0
 ZeroDivisionError: integer division or modulo by zero
I suppose that the specification should be extended such that the above to get transformed to:
 a = lambda: 1/0
 #ERROR>>> a()
 #
 #Traceback (most recent call last):
 #....
or something similar. Thoughts?

Interesting example. This issue is a bit more complicated than I thought. Clearly, the call that reveals an error in previous lines should not be simply deleted.

#21140 is about saving Output Window (renamed) as .txt instead of .py. Same method should be used to save shell log as .txt. My idea is that File menu for shell window should, if possible, have both
Save as log
Save as runnable code

This should be easier to do with the new shell with indents fixed.

In #45297, Steven D'Aprano suggests deleting code immediately followed by traceback. (SyntaxErrors should not be there at all -- another issue.) But should NameError, for instance, be ignore, just because user printed something? Or block removed just because it comes before print statement?
Without more feedback, I believe most would want all code actually run. If there is a Traceback, Add comment with error and message.
UI is a tough issue. I don't want to add more File menu entries and hot keys. We can add to shell context menu as have already done.
Maybe this: after getting the save name, branch on type: .py, code only; anything else, full log. Subsequent ^S saves use last save-as name to decide.