Everyone else has already had excellent things to say, so I'm tossing in my two cents not as an argument, but more like just something else to chew over.
"Vietnam" is the only time I can think of where Sam flatly did not accomplish his mission. His mission, according to Ziggy, was to rescue the MIAs. Sam wanted his mission to be to save his brother's life. He did, but at the expense of Maggie's life, and at the expense of Al's freedom. So he learned a lesson about sticking with the right mission.
From a behind-the-scenes persceptive, I think Bellisario was interested earlier in the series with the suspense being on "What if Sam doesn't leap? What if he's stuck living this other person's life forever?" At some point, though, it became obvious that Sam was going to leap every time, so Bellisario changed the focus to the more suspenseful idea: "What if Sam doesn't accomplish the mission?"
Of course, as mentioned, there are Sam's bittersweet victories (Freedom, Good Night Dear Heart, MIA, Leap Home Pt. 1, Black on White on Fire, Last Dance Before an Execution, Trilogy Pt. 1, etc.), as well as the times when history looped back on itself. There are three examples of this, which I list below.
In "Deliver Us from Evil," Sam didn't actually leap back in to change anything, only to find that he had prevented Alia from ever being there in the first place. (Which raises the question, why didn't that happen again when history changed for the better in EL II/III? But that's a whole 'nother topic...)
In "Mirror Image," Sam didn't leap back in to Jake from "MIA," he just leaped in as himself at the moment after he left the scene. (Which raises another interesting question, which I'll start another thread for.)
And the one I'm surprised no one mentioned yet--"The *********." (Maybe no one mentioned it because of the name. Should I call it "the Halloween episode" instead?)
In this case, history does actually seem to loop back on itself, and Sam gets a second chance to put things right. In this fascinating scenario, simply stopping Tully's death was enough of a chain reaction to prevent everything else from happening--even though the deaths were unrelated to each other, and in theory, "Al" could have made another attempt on Tully's life, or just started killing the others.
Of course, it's possible that the whole episode was just a dream--or, if you will, a vision given to him by GFTW so that he would know how to stop the whole thing in the first place. But Al did say that PQL lost contact with Sam completely for a few minutes...which suggests that Sam was briefly taken
outside of time in order to make the second leap.
One final note: by the time of LHO, who knows what Bellisario was thinking? He also has Al remind Sam of the time they switched places--even though, according to Al himself in "The Leap Back," Sam doesn't remember anything of the experience, and reminding Sam of that runs the danger of reminding Sam of Donna! So was Al lying, or...
Ooof. My head's spinning. I think I need chocolate now.