>> I believe this patch is a change for the better:
>
> Could you resend it as unified diff? Or push to
> a branch. diff-context->unified doesn't seem to work on the patch you sent.

I thought maybe context diff is easier to read in this case,
but here is unified diff below.

>> 1. makes next-error-function buffer-local
>
> Interesting.
>
>> 2. sets both buffer-local and global values
>
> Why? If next-error-find-buffer-function can find the appropriate buffer, it
> can use the local value in it.

We need the global value as well to get the last next-error buffer
when there is no buffer-local value yet in the current buffer.

>> 3. adds customizable next-error-find-buffer-function
>>
>> 4. moves window-on-frame-visibility code to separate function
>>     that can be used to customize for backward-compatibility
>
> Do we get a built-in alternative to this value? If we just provide
> a customization point, that nice, but not a significant improvement.

You mean to remove next-error-buffer-on-selected-frame?
Or maybe to do the other way: add more predefined functions like
a function to use window-local navigation as an alternative.

>> 5. adds next-error-select-buffer to manually switch to another
>>     next-error capable buffer
>
> Not having tried the patch yet... Will the user have to do that after
> semi-accidentally opening a changelog-mode buffer, in order not to switch
> to its error list?

When the user visits a ChangeLog buffer from *grep*, then
next-error continues the *grep* navigation.  When the user
visit a ChangeLog file by any other command, then next-error
navigates entries in that ChangeLog buffer.

But in case when the user changes mind and decides to switch
from *grep* navigation to ChangeLog navigation, there is
this new command.

>> 6. message to show which next-error buffer is currently used
>
> Every time we call `next-error'?

That's right.