While thinking about Bug#17376 I noticed some related bugs, which appear 
to have been in 'grep' since at least grep 2.0.  For example:

$ encode() { echo "$1" | tr ABC '\357\274\241'; }
$ encode ABCABC >exp3
$ encode _____________________ABCABC___ >exp4
$ bca=$(encode BCA)
$ grep "$bca" exp3
$ grep -F "$bca" exp3
$ grep "\\(\\)\\1$bca" exp3
ＡＡ

Here the regexp code disagrees with KWset and with the DFA, which is a 
bug: KWset and DFA should affect only performance, not behavior.

$ grep "$bca" exp4
_____________________ＡＡ___
$ grep -F "$bca" exp4
_____________________ＡＡ___
$ grep "\\(\\)\\1$bca" exp4
_____________________ＡＡ___

Here they agree, but only because there's a bug in is_mb_middle!
Fixing that will cause them to disagree again.

I installed the attached patch to fix the bugs I found, and to adjust 
the test cases accordingly.