I tried doing a backup for the first time since upgrading to 1.77b. At first, my attachments directory didn't allow writing so no file was created. There also was no error message. I set the permissions of attachments to 777 and then the backup would create a file, named correctly, that was empty. Further investigation showed that it was trying to execute the command 'no mysql/mysqldump ...'. It looks like the changes in the detection code works worse for me that the old code. I commented out the changes in detectsqlpath() as well as some of the changes in the $write area of editconf.php and it then worked as it did before.
I now see where I could hard-wire this path in the config.php file, but thought you'd like to know about my experience.