If God can do anything can he make a mistake?

Indeed. But the point of Sagan (and Flew's) analogies is, still, simply that unique claims of any sort about a being qualified into existence are basically just offering excuse after excuse why the burden of proof is not discharged until falsification is effectively impossible. I hope that helps. (And I see you are still dodging the bullet when I suggest that an invisible being that can do the impossible can, well, do just that and thus be both unambiguously visible and invisible lol.)

See my final words below. The actual original premise actually leads with 'if God can do anything...' Any certainty here is all yours. Look back and check. Is that something "I failed to mention" before?

And, as has been pointed out to you with good logical reasons, the premise is, quite simply a false one. To accept it as valid, as it appears you do with that "my argument" above, is to misunderstand the way biblical scholars and thinkers commonly view the nature of an 'all-powerful' deity. Sorry about that. The point is, still, that to go on as one might and argue in favour of that type of god, inevitably leads to qualifying such a being into existence, as I have shown ... a process of special pleading that we are surely all over-familiar with elsewhere.

In short, what you are so taken with here is a duff idea, one inevitably propped up by with logic-busting special pleading ('... so a triangle can have four sides if ever God wills it' 'God can lift rocks that He made that are unliftable' etc). I can't falsify such assertions, other with logic, which of course is rendered useless by qualifying a supreme being as one which, being special, of course can do the illogically incoherent, can't it now? 

I don't refuse it. I refute it- but only when, as you have done, it is taken as an absolute, rather than the conditional, statement that the original poster submitted.  And even then only when normal rules of logic apply, without special pleading.