criticals will happen an awful lot less, this is an overall good thing to my mind (crits are much worse for players, I have killed a few characters this way), but those that love a keen weapon might be upset. (though what I would do is say that you only need one 10 to get a possible crit (which would make them about the same power they are now... However as crits would diminish dramatically in frequency it would make them relatively more powerful...
taking 20 could be replaced with you get 10 + 1d10 (instead of the 16/18 suggested) which would still leave the result a bit in question, but still heavily sway the result in their favour...
The other result would be that the third and fourth attacks in an itterative attack would have very little chance of connecting, and spells with high DC saves would be even more powerful... so essentially I fear this system might sway things even further in the casters favour... Might work for 4e, but I think it might punish melee types too much in 3e.