It's actually quite easy to see how Sauron at least influenced the lust Saruman developed for power, for it is told that his quest for knowledge brought him ever closer to probing the mind of the Enemy, which, as you can imagine, would put one at risk of being corrupted. I think it would be safe to say that Sauron did not corrupt Saruman, or bend him to his will (as, say, he did with the Nazgul), but he may have helped to awaken that inner greed and lust for power, which Saruman did not always have.
The limiting of the powers of the Istari may have prolonged the war with Sauron, but if Saruman was more powerful, he may have found the Ring and laid waste to Rohan, and perhaps the Ents as well. Without the aid of the Rohirrim, Sauron would have crushed Gondor, and then the Dark Lord would have waged a great war with Saruman, which would have further desecrated the land and any surviving people.
If we look at the powers of the Istari, they are all about "influence", which another poster mentioned above. Gandalf is the great "meddler of affairs", first getting a nice innocent hobbit to go on an adventure with him and his dwarves (resulting in the finding of the Ring [which perhaps the Valar had fated to happen through Gandalf's intervention]); then there is the Council of Elrond, which Gandalf plays a pivotal role in; then the trip to Rohan, where he breaks the dominion of Saruman and, in effect, influences Theoden to go forth to war (I dare say he may even have deliberately left the hobbits with Treebeard, knowing that they were perhaps the small stones that start an avalanche); and that's not even mentioning Minas Tirith. Indeed, his Ring is said to amplify his own power to influence.
And what of Saruman? The Voice of Saruman is a great example of a power to influence, and the leech-craft of Grima is an extension of Saruman's attempts to influence and dominate. Indeed, even Radagast could be said to have the power of influence, for it is with this that he has such rapport with the birds and beasts of the land.
Then there are the two Blue Wizards. We do not know much about these, but there is rumour that they went into the East and fell under the dominion of Sauron. If this is so, they became his servants (or were destroyed and their power assimilated by him). If they were more powerful, this may have made an even greater threat.
-D