Sauron does indeed have the ability to distort what others see, as he does with Denethor; but that does not by itself imply that he has the power to show what is not at all there—Gandalf says of the Seeing-Stones for example:
'The Stones of Seeing do not lie, and not even the Lord of Barad-dûr can make them do so. He can, maybe, by his will choose what things shall be seen by weaker minds, or cause them to mistake the meaning of what they see.'
(The Lord of the Rings, The Return of the King, Book V, Chapter 9, "The Last Debate")
On the other hand, Sauron seems to have done just this sort of illusionment during the First Age, to deceive Gorlim, companion of Barahir:
Now among the companions of Barahir was Gorlim son of Angrim. His wife was named Eilinel, and their love was great, ere evil befell. But Gorlim returning from the war upon the marches found his house plundered and forsaken, and his wife gone; whether slain or taken he knew not. Then he fled to Barahir, and of companions his he was the most fierce and desperate; but doubt gnawed his heart, thinking that perhaps Eilinel was not dead. At times he would depart alone and secretly, and visit his house that stood amid the fields and woods he had once possessed; and this became known to the servants of Morgoth.
On a time of autumn he came in the dusk of evening [to the house he had formerly occupied], and drawing near he saw as he thought a light at the window; and coming warily he looked within. There he saw Eilinel [his wife], and her face was worn with grief and hunger, and it seemed to him that he heard her voice lamenting that he had forsaken her.
Sauron uses the illusion to capture Gorlim and convince him to betray Barahir.
Thus it is at least theoretically possible that what Frodo sees from Amon Hen is an illusion.
However, the Gorlim illusion was set up after Sauron became aware (directly or indirectly) of his existence and habits; Sauron was (as another answer points out) unaware of Frodo's presence on Amon Hen until Frodo actually gazed on Barad-dûr. It therefore appears that indeed Frodo's vision did reflect the truth, at least in some sense. Let's then consider the actual signs of strife referred to in the text.
Orcs in the Misty Mountains: This is quite simple. The text here reads "The Misty Mountains were crawling like anthills: orcs were issuing out of a thousand holes." This simply echoes and amplifies a quote from "The Shadow of the Past" (Book I, Chapter 2):
Orcs were multiplying again in the mountains.
Fighting in Mirkwood and the land of the Beornings: I combine these two since the Beornings control the land roughly between the Misty Mountains and Mirkwood. The text you quote states:
Under the boughs of Mirkwood there was deadly strife of Elves and Men and fell beasts. The land of the Beornings was aflame.
Again, "The Shadow of the Past" does indicate very roughly that "away far east and south there were wars and growing fear". Certainly, an increase in the orcs of the Misty Mountains would lead to increasing strife with the Beornings, who owned and controlled the lands nearby; and Glóin admits before the Council of Elrond that
If it were not for the Beornings, the passage from Dale to Rivendell would long ago have become impossible.
(The Fellowship of the Ring, Book II, Chapter 1, "Many Meetings")
As far as Mirkwood itself, Legolas admits at the Council of Elrond that
The dark things that were driven out in the year of the Dragon's fall have returned in greater numbers, and Mirkwood is again an evil place, save where our realm is maintained. ... Dol Guldur ... is still a very evil place; we do not go that way.
It is not unreasonable to believe that "maintenance of the realm" would thus require "strife of Elves and Men [with] fell beasts". (Why would Men be involved? The realm of the Beornings extends all the way to the western edge of Mirkwood; they'd be involved in any fighting in that area.)
A cloud over Moria: This vision occurs, according to Appendix B, on 26 February 3018; Gandalf cast down the Balrog on 25 January. It's not entirely clear why there would still be a "cloud" over Moria if this were solely the physical cloud created by the literal fall of the Balrog; but a cloud there had been; and perhaps this is simply a foreshadowing by Tolkien of Gandalf's overthrow of his enemy.
Smoke on the borders of Lórien: More difficult to explain, at least in ordinary physical terms. We're not told of any active fighting going on in or near the forest at that time, or indeed for quite a while (Appendix B dates the first assault on Lórien to 11 March). It's not clear what exactly is being referred to here.
Horsemen in Rohan; wolves from Isengard: Undoubtedly this refers to the First Battle of the Fords of Isen, which took place the day before Frodo's vision (25 February), and Éomer says at his first meeting with the Three Hunters that "There is trouble now on all our borders, and we are threatened ... At that time [when Gandalf visited, the previous summer] our trouble with Saruman began" (The Two Towers, Book III, Chapter 2, "The Riders of Rohan").
Chariots, warships, and armies out of Rhûn and Harad: Given their appearance at the Battle of the Pelennor Fields, it's obvious that they'd be appearing round about this time.
Thus, yes, this was overall an accurate vision, though not stated in very precise terms; most or all of what was seen is reflected in other statements in either the narrative of the book or else the Appendices.