How has Ulfric Stormcloak failed?
First off, im not immensly wrapped up in the civil war thing, but I lean toward anyone who wants his people to be Independent from an opressor, Empire (Thalmor).
Other than letting a few nord bandits walk around, the guy really pisses excellence. I'd rather have that than letting some thalmor inquisition grabbing innocent people and making them dissapear. If the Empire would be allowed more power the thalmor's influence on the Empires actions itself would swell.
So the moral of the story is, Ulfric ain't so bad.
My comment on his failure is that of basic strategy. His enemy is the Thalmor, pretty much all humans hate them. Rather than focus on fighting the Thalmor he's instead started a war that will weaken the enemies of the Thalmor no matter who wins. This is an unnecessary war. That's a failure, and a pretty basic failure. The only reason why'd he do that is stupidity or because he desires the title of High King so much. Heck, the High King's Court Wizard, who practically knew him since birth, thought there was a better than decent chance that he High King would join in leaving the Empire and going against the Thalmor. Rather than even TALK about that with the High King, Ulfric challenged and killed him. Note, that he could have talked first and only challenged if necessary, if one thinks a challenge was a good idea at all.
Obviously a better strategy would be forming a covert resistance against the Thalmor, striking Thalmor targets within the Empire and working to unite popular and official positions to fighting off Thalmor influences. It's not like this would necessarily be very hard. Empire forces HATE the Thalmor and they don't like the treaty either, but it isn't like there was much of a choice at the time.
Fighting oppressors is certainly a good thing, but the Empire isn't the oppressor here. They were forced into a treaty with the Thalmor, who are the occupying force. Of course, they weren't occupying Skyrim at all before the rebellion and Talos worship was banned in name only before the rebellion started and the Thalmor used that as an excuse to come into Skyrim. There's a decided LACK of fighting the actual oppressors here, and instead a focus on fighting other natives of Skyrim and deposing popular and good leaders because they don't side with the Stormcloaks. So it isn't like the Stormcloaks are all about giving the people what they want...the eventual goal isn't freedom for everyone, but Ulfric as High King and people who support him replacing all the Jarls who don't.
In some respects, Ulfric's heart is in the right place. But his methodology is crap on many levels.