I think it's location early in the third movie indicates what Peter Jackson was trying to do with it:
---They just beat Isengard and won at Helm's deep, so viewers need a cue that there is still a bigger danger ahead, something Gandalf hasn't even seen.
---Saruman is visibly connecting this thought with the Palantir.
---In a scene that isn't much further away, one of the Hobbits dangerously looks into the same Palantir, and sees the extreme danger that Minis Tirith is in. The tree, the eye, flames, all that stuff.
---From that point the protagonists prepare to save Minis Tirith. Gandalf rides there to warn them and light the beacons for help, Aragorn eventually makes his way to summon the army of the dead to help save Minis Tirith, and Rohan begins its muster for war.
---Minis Tirith nearly falls because of its hopeless leader (Denethor), over-matched forces, and internal weakness.
---Everthing comes together at the right time to save the city, Gandalf has the hobbit light the beacons, Rohan arrives, prophecy is fulfilled in Eowyn's killing of the Witch King, Aragorn arrives with the army, etc.
I think we see the plot device that Saruman's quote was supposed to be: it cued the audience that a problem was still ahead. That problem turned out to be two-fold, (A) Sauron planned to launch a massive onslaught against Minis Tirith and cripple his opposition, and (B) Minis Tirith was too weak from its leadership down to survive such an onslaught. That is what Gandalf, Aragorn, and Rohan rectify before the movie turns to the final movement at Mordor, both at the Black Gate and with the hobbits at Mt Doom.