A 1 being a critical miss on a skill check makes sense to me. I think checks should be defined as an action that always has a chance of failure. Otherwise there is no check-- you don't roll to breathe, to walk each step in town, etc. However, I do not like 20 as an automatic success, because chance of failure does not always imply chance of success.
For me there are two big problems with this rule:
#1) This is going to lead to annoying arguments for the DM, because there will obviously be cases where the PCs cannot succeed at something. So either the DM withholds checks, leading to arguments from players who think they should be allowed to always make Diplomacy checks etc., or the DM allows it and tries to "cheat" a player out of his well-earned 20, resulting in more arguments.