A poor DM does not run what I'll call a playiable game. An average DM will, but an average DM could in 1e as well. A DM needs to be good to run a good game because the ruleset is not everything in a game. A DM needs to do a lot more then deal with the rules.
I disagree. The rules in 3e will handhold you well enough that you can play a playable game, even if the DM isn't very good. It may not be a great game, it may be pure hack, but, it's still playable.
Take this as a f'instance. In the 2e PHB there is a section for playing priests of a specific mythos. It states right in that section that the DM and player will have to sit down and hammer out the class. Beyond that, not much guidance is given.
So, if I want to play a priest of Thor, I sit down with my DM and work it out. If the DM is good, then no problems. If the DM is bad, then I wind up with a workable character, a character that is overpowered or a character that is underpowered. The odds of me getting a workable character are that much smaller and the odds that either I'm going to overshadow everyone else's character because I'm Priestzilla, or that I'm going to be sitting in the corner not doing much are that much higher.
In 3e, we write "Cleric of Thor" on the character sheet, give him Strength and Weather domains and we're good to go. Good, bad or indifferent, the DM will most likely come to this conclusion. And, because we're working from a ruleset that is functionally balanced, we can know beforehand that my character will be viable and will not play havoc with someone's game.
And that's just pulling an example from the Player's Handbook. Never mind if I start tossing in Kits into the mix. Or the 1e Unearthed Arcana. Or start pulling goodies from Dragon. Howzabout a 1e bard? Make him a half elf and you get to bard PDQ. Maybe I "roll" really well and get psionics.
Because earlier rulesets had these huge campaign bombs that could really disrupt a campaign, the quality of the game hinged so heavily on DM ability.
I've been told time and time again that 3e takes power away from the DM and gives it to the rules. I agree with that. But, if that's true, then the abilities of the DM become somewhat less important (but not unimportant of course) to the quality of the game. Seems like a logical chain. DM has less direct impact on the characters due to the structure of the rules therefore the abilities of the DM have less impact on the game.
Yes, a DM needs to do a lot more than deal with the rules. But, if the rules are an issue, then the DM needs to deal with them. Thus the DM's abilities become more important. When the rules are less of an issue, then the DM doesn't need to deal with them and his abilities become less important.
Now, how much less is a matter of opinion. But, it will be less nonetheless.