I dont really know why people would have such a hard time accepting the fact that they are fallible (esp. when many here in the US self-identify as Christian and doctrine dictates that humans are flawed)...
Any time I take on a task I immediately start devising in my head the best way to accomplish it - and do my best to think of ways that the work will better serve me in the future (i.e. if the product may be re-used I try to make sure that it is easily manipulated for future use)... As soon as I start working on something new I often immediately recognize things that could have made the task easier - I just make sure to take note of them. So long as you are capable of acting also as an observer when doing your work - you can optimize your work much more easily (I realize this seems like common sense).
Simple examples of this can be encountered just about any time someone uses a new tool or does a routine household job for the first time (especially when fabricating something). You dont need a catastrophic failure to realize you can improve your process (changing out a wax ring on a toilet the FIRST time seemed much harder than say the 4th time since I streamlined the process)...
The main thing people need to realize is not necessarily their failures, but the fact that no one is perfect - and people arent going to do things the best and/or easiest way the first time. Once you know that you can start taking steps to improving your process - whether its something you have done before or a new task that bears at least some similarity to something you have done in the past.