I'm pretty confused. During the fight between Obi-Wan and Count Dooku on Geonosis, Obi-Wan is doing fine until he gets a little cut on his arm, and a little cut on his leg. Then he's down. I don't get it. If Obi-Wan was such a great Jedi, how did such little injuries bring him to the ground?
I don't think there is a direct canon answer to your question; but Lightsaber combat is basically about immersing yourself in the Force and concentrating (too many canon sources to back that fact. For example, see ROTS novelization describing various fights of Obi-Wan, Mace Windu and Anakin as a random example).
Thus, if you are injured, if you let your concentration slip, it can have a drastic effect on your combat abilities.
Also, your implication that "he was doing fine" is contrary to the screenplay - Obi-Wan was outmatched from the beginning, even if the visuals didn't make it obvious in the movie:
OBI-WAN comes in fast, swinging at COUNT DOOKU's head. DOOKU parries the cut easily. As they fight, it quickly becomes clear that DOOKU is the complete swordsman, elegant, graceful, classical - a master of the old style.
COUNT DOOKU: Master Kenobi, you disappoint me. Yoda holds you in such high esteem.
COUNT DOOKU parries another cut and then thrusts. OBI-WAN steps back quickly, panting for breath.
COUNT DOOKU: Come, come, Master Kenobi. Put me out of my misery.
OBI-WAN takes a deep breath, gets a fresh grip on his lightsaber and comes in again. For a moment, he drives COUNT DOOKU back. Then DOOKU's superior skill begins to tell again, and he forces OBI-WAN to retreat.
COUNT DOOKU increases the tempo of his attack. OBI-WAN is pushed to the limit to defend himself. DOOKU presses. His lightsaber flashes.
OBI-WAN is wounded in the shoulder, then the thigh. He stumbles back against the wall, trips, and falls. His lightsaber goes skittering across the floor.
This makes sense, if you recall that Dooku was considered a premier swordsman in the Jedi Order, even before becoming Palpatines Sith Apprentice:
JOCASTA NU: He was always striving to become a more powerful Jedi. He wanted to be the best. With a lightsaber, in the old style of fencing, he had no match. His knowledge of the Force was... unique
Remember that Dooku was Qui-Gon's Jedi Master, who was Obi-Wan's.
The hits that you refer to are called shiim, minute wounds that are the sign of either desperation, or as in this combat, domination.
Dooku was a master of Form II lightsaber combat, a more dueling centric form of lightsaber combat than the Form III lightsaber combat Obi-wan employed, and these wounds showed his complete mastery over the Jedi. The difference is supposed to be shown in the economy of motion that Dooku employed, even when on the defensive, vs the comparatively wider and less controlled arcs of Kenobi.
The wounds didn't cause his fall, they merely presaged it. In the end, it was a combination of positioning and mastery on the part of Dooku, and Obi-Wan's extreme effort in keeping up with the Sith's greater skill that precipitated the seemingly sudden reversal of fortunes. In truth, it was telegraphed during the whole of the fight, thus the taunting nature of the dialog from Dooku during the engagement.
The lightsaber's blade is pure energy, at a very high temperature, enough to easily melt metal. It didn't just cut Obi-Wan, it burned his flesh. I bet it hurt. No wonder the guy as incapacitated for the rest of the fight. Also, I think that the fact that Obi-Wan had fought the battle of Geonosis just before his duel with Dooku, probably being very tired, contributed a lot to his defeat. He probably would have put up a much better fight had he been physically at 100%.
According to the film's junior novelisation, Kenobi, after being struck by Dooku's lightsaber, was in a considerable amount of pain as well as being physically drained by his efforts with the Force and by the fight itself. He pretty much passes out after throwing his lightsaber to Anakin.
But Dooku is right, Obi-Wan thought through the haze of pain and exhaustion. Anakin is no match for him … unless Anakin does something unexpected. Using all his remaining strength, he reached out with the Force. “Anakin!” he called, and flung his lightsaber to his apprentice.
Yoda could feel the two exhausted, injured Jedi reaching for the Force to keep the crane from falling, but they did not have enough strength left.
Something which is backed up by the film's official novelisation
Obi-Wan knew that he had to do something. He tried to come forward, but winced and fell back, in too much pain. As he collected his thoughts, he reached out with the Force instead, grabbing at his lightsaber and pulling it in to his grasp. “Anakin!” he called, and he tossed the young Padawan the blade. Anakin caught it without ever breaking the flow of his fighting, turning it under and igniting it immediately, putting it into the swirling flow.
Note that they're not just fighting with swords, but also drawing on strength from the Force, something that can leave you drained to the point of death (and potentially beyond).
With a sudden burst of sheer power, Master Yoda flew forward, his blade working so mightily that its residual glow outshone even those of both of Anakin’s lightsabers when he was at the peak of his dance. Dooku held strong, though, his red blade parrying brilliantly, each block backed by the power of the Force, or else Yoda’s strikes would have driven right through.