A botched update that failed halfway is causing issues, I was wondering how I could roll back an update for SQL Server? Secondly, I was wondering if there is any other place (aside from) **Setup Bootstrap\Log** where I could see which updates were installing and which one failed. I use SQL Server 2012
That path is the full source of SQL installation info and is a goldmine.
The best way to deal with a failed patch is to find out what happened; either in those files or the SQL ERRORLOG. It's most commonly SSISDB in an availability group or a filestream error (fixable with add/remove programs on the instance to run a repair).
I'm not sure if you can rollback an unsuccessful patch but it's easy to reapply the patch and try again, they resume very very well. After its successfully installed then they're easy to uninstall with add/remove programs again.
There aren't many good reasons to uninstall an SP or CU for SQL though. They're pretty important.