I know he used his power to slow down Legolas, Aragorn and Gimli but do we get any other hints of him using his personal power?
Very little. The only magical ability Saruman displays consistently is his persuasive Voice. Pippin and Aragorn have a conversation about this in The Two Towers, suggesting that Saruman is less powerful than he used to be:
I don't know what Saruman thought was happening; but anyway he did not know how to deal with it. His wizardry may have been falling off lately, of course; but anyway I think he has not much grit, not much plain courage alone in a tight place without a lot of slaves and machines and things, if you know what I mean. Very different from old Gandalf. I wonder if his fame was not all along mainly due to his cleverness in settling at Isengard.'
'No,' said Aragorn. 'Once he was as great as his fame made him. His knowledge was deep, his thought was subtle, and his hands marvellously skilled; and he had a power over the minds of others. The wise he could persuade, and the smaller folk he could daunt. That power he certainly still keeps.
The Two Towers Book 3 Chapter 9: "Flotsam and Jetsam"
Fellowship of the Ring
Gandalf hints that Saruman's power was particularly helpful in expelling Sauron from Dol Guldur:
Saruman has long studied the arts of the Enemy himself, and this we have often been able to forestall him. It was by the devices of Saruman that we drove him from Dol Guldur.
Fellowship of the Ring Book 2 Chapter 2: "The Council of Elrond"
The Two Towers
The breeding of the Uruk-hai is maybe an example of Saruman exerting his power, but it's unclear. On the surface it seems like your basic everyday cross-breeding, but then magic in Tolkien is typically a good deal more subtle than in most high fantasy settings, so maybe. Your mileage may vary.
As pointed out in the question, Aragorn and Legolas attribute their difficulty in chasing the Uruk-hai to Saruman's power:
'There is something strange at work in this land. I [Aragorn] distrust the silence. I distrust even the pale Moon. The stars are faint; and I am weary as I have seldom been before, weary as no Ranger should be with a clear trail to follow. There is some will that lends speed to our foes and sets an unseen barrier before us: a weariness that is in the heart more than the limb.'
'Truly,' said Legolas. 'That I have known since we first came down from the Emyn Muil. For the will is not behind us, but before us.' He pointed away over the land of Rohan into the darkening West under the sickle moon.
'Saruman!' muttered Aragorn. 'But he shall not turn us back!
The Two Towers Book 3 Chapter 2: "The Riders of Rohan"
Saruman probably visited Aragorn, Legolas, and Gimli as they camped by Fangorn Forest, and disappeared without a trace:
Suddenly Gimli looked up, and there just on the edge of the firelight stood an old bent man, leaning on a staff, and wrapped in a great cloak; his wide-brimmed hat was pulled down over his eyes. Gimli sprang up, too amazed for a moment to cry out, though at once the thought flashed into his mind that Saruman had caught them. Both Aragorn and Legolas, roused by his sudden movement, sat up and stared. The old man did not speak or make a sign.
'Well, father, what can we do for you?' said Aragorn, leaping to his feet. 'Come and be warm, if you are cold!' He strode forward, but the old man was gone. There was no trace of him to be found near at hand, and they did not dare to wander far.
The Two Towers Book 3 Chapter 2: "The Riders of Rohan"
He tries to use his Voice on Théoden when confronted at Isengard:
Théoden opened his mouth as if to speak, but he said nothing. He looked up at the face of Saruman with its dark solemn eyes bent down upon him, and then to Gandalf at his side; and he seemed to hesitate. Gandalf made no sign; but stood silent as stone, as one waiting patiently for some call that has not yet come. The Riders stirred at first, murmuring with approval of the words of Saruman; and then they too were silent, as men spell-bound. It seemed to them that Gandalf had never spoken so fair and fittingly to their lord. Rough and proud now seemed all his dealings with Théoden. And over their hearts crept a shadow, the fear of a great danger: the end of the Mark in a darkness to which Gandalf was driving them, while Saruman stood beside a door of escape, holding it half open so that a ray of light came through. There was a heavy silence.
The Two Towers Book 3 Chapter 10: "The Voice of Saruman"
That entire chapter is replete with examples of Saruman using this power, and I chose only one quote. There are many, many more.
Return of the King
He uses his voice on the hobbits who came to expel him from the Shire:
Saruman looked round at their hostile faces and smiled. 'Kill him!' he mocked. 'Kill him, if you think there are enough of you, my brave hobbits!' He drew himself up and stared at them darkly with his black eyes. 'But do not think that when I lost all my goods I lost all my power! Whoever strikes me shall be accursed. And if my blood stains the Shire, it shall wither and never again be healed.'
The hobbits recoiled. But Frodo said: 'Do not believe him! He has lost all power, save his voice that can still daunt you and deceive you, if you let it. But I will not have him slain. It is useless to meet revenge with revenge: it will heal nothing. Go, Saruman, by the speediest way!'
Return of the King Book 6 Chapter 8: "The Scouring of the Shire"
Immediately after this he "predicts" that Frodo will have neither health nor long life. It's not clear whether Saruman is actually using a gift for prophecy, or if he just knew that Frodo had been stabbed with a Morgul-blade and made an educated guess.
Saruman appears to use his Voice on the Witch-King, when he came to Isengard to inquire about the Shire:
Two days after Gandalf had departed from Orthanc, the Lord of Morgul halted before the Gate of Isengard. Then Saruman, already filled with wrath and fear by the escape of Gandalf, perceived the peril of standing between enemies, a known traitor to both. His dread was great, for his hope of deceiving Sauron, or at the least of receiving his favour in victory, was utterly lost. Now either he himself must gain the Ring or come to ruin and torment. But he was wary and cunning still, and he had ordered Isengard against just such an evil chance. The Circle of Isengard was too strong for even the Lord of Morgul and his company to assail without great force of war. Therefore to his challenge and demands he received only the answer of the voice of Saruman, that spoke by some art as though it came from the Gate itself.
"It is not a land that you look for," it said. "I know what you seek, though you do not name it. I have it not, as surely its servants perceive without telling; for if I had it, then you would bow before me and call me Lord. And if I knew where this thing was hid, I should not be here, but long gone before you take it. There is one only whom I guess to have this knowledge: Mithrandir, enemy of Sauron. And since it is but two days since he departed from Isengard, seek him nearby."
Such was still the power of the voice of Saruman that even the Lord of the Nazgûl did not question what it said, whether it was false or short of the full truth; but straightway he rode from the Gate and began to hunt for Gandalf in Rohan.
Unfinished Tales Part 3: The Third Age Chapter 4: "The Hunt for the Ring" (i) Of the Journey of the Black Riders according to the account that Gandalf gave to Frodo
I think his ability to use the Palantíri could have also been a power displayed. He can use it no problem but when Pipen attempts in The Return of the King, He gets messed up a little. This could simply be from fear but possibly from the overwhelming power from the Palantíri.