I think I have a simular problem I had before with utils.inc.php.
When I wanted to go for the sitemap building, this is what I get:
Warning: require_once(/public_html/inc/classes/BxDolSiteMapsPages.php) [function.require-once]: failed to open stream: No such file or directory in /public_html/inc/utils.inc.php on line1023
Fatal error: require_once() [function.require]: Failed opening required '/public_html/inc/classes/BxDolSiteMapsPages.php' (include_path='.:/usr/lib/php:/usr/local/lib/php') in/public_html/inc/utils.inc.php on line 1023
BxDolSiteMapsPages.php is not in the directory and it was not there before the update as well.
What could cause the problem?
Your missreading the error. The problem is not in inc/utils.inc.php. The error states a function being called from that file is not found. Meaning it can't find public_html/inc/classes/BxDolSiteMapsPages.php
So you do not want to look in the inc folder for BxDolSiteMapsPages.php you want to look in inc/classes to make sure BxDolSiteMapsPages.php is there.
BxDolSiteMapsPages.php was new to dolphin 7.1.1, not 7.1.2. It will not be found in the 7.1.2 patch because it was not updated in that patch, so if the file is missing you will need to get a full dolphin zip file to get that file from because it's not part of the patch.
I am guessing that because your inc folder was not writable that none on the files in the classes folder got updated either.
The inc folder is suppose to be 777 during dolphin install, but if you remember the permissions on that folder are to be made non writable after the install is done(permission reversal). Which most people forget about.
The fact that FTP could not over write the files indicates you used the wrong permission setting when the permissions were reversed. The mode is not suppose to be publicly writable after install, but it is still suppose to be writable by the owner. So the proper mod for the inc folder should be 755
If i were you i would get a full install zip file of 7.1.2 and re-upload the entire inc folder just to make sure everything got replaced. I am guessing you have more files that are outdated as well even if your not seeing any errors. Some files are just to fix bugs, and in those cases you would not see any errors.