There is no evidence to suggest that it was poisonous¹.

_{¹At least not in the way you may be interpreting the word poisonous. No, walking into Mordor would not kill you and breathing the fumes would not kill you. There were gasses and smells in Gorgoroth that were unpleasant and thick. Which, weighed down on our heroes. But they weren't being poisoned.}

The smoke in Gorgoroth, "the valley of Terror", is noted throughout the Lord of the Rings. It is accepted that Orodruin was spewing out gasses which choked the lands of Gorgoroth and veiled it in mystery.

...and it looked upon Gorgoroth, the valley of terror in the Land of Mordor. Darkness lay there under the Sun. Fire glowed amid the smoke. Mount Doom was burning, and a great reek rising.
_{The Fellowship of the Ring - Book II, Chapter 10: The Breaking of the Fellowship}

The twilight deepened as great vapours rose in the East and crawled above them.
_{The Two Towers - Book IV, Chapter 7: Journey to the Cross-roads}

'No water flowing out of Imlad Morgul, were his words,' said Frodo. `We are not in that valley now, and if we came on a spring it would be flowing into it and not out of it.'
'I wouldn't trust it,' said Sam, 'not till I was dying of thirst. There's a wicked feeling about this place.' He sniffed. 'And a smell, I fancy. Do you notice it? A queer kind of a smell, stuffy. I don't like it.'
_{The Two Towers - Book IV, Chapter 8: The Stairs of Cirith Ungol}

Before them towards Mordor lay like a moat a great mire of reeking mud and foul-smelling pools.
_{The Return of the King - Book VI, Chapter 10: The Black Gate Opens}

That being said, the air in Mordor, certainly had a foulness about it:

'... Last time I looked I’d got about enough of that waybread, and of what Captain Faramir gave us, to keep me on my legs for a couple of weeks at a pinch. But if there’s a drop left in my bottle, there’s no more. That’s not going to be enough for two, nohow. Don’t orcs eat, and don’t they drink? Or do they just live on foul air and poison?'
_{The Return of the King - Book VI, Chapter 1: The Tower of Cirith Ungol}

Again, as they approach Mount Doom, the air seems thicken and take more of a toll. While at this stage in the journey Frodo and Sam have run low of water and food, and the weight of the ring is at it's greatest, the air still seems to be affecting them.

The last stage of their journey to Orodruin came, and it was a torment greater than Sam had ever thought that he could bear. He was in pain, and so parched that he could no longer swallow even a mouthful of food. It remained dark, not only because of the smokes of the Mountain: there seemed to be a storm coming up, and away to the south-east there was a shimmer of lightnings under the black skies. Worst of all, the air was full of fumes; breathing was painful and difficult, and a dizziness came on them, so that they staggered and often fell. And yet their wills did not yield, and they struggled on.
_{The Return of the King - Book VI, Chapter 3: Mount Doom}

It must be noted, however, that Frodo would not call it poison, stating the do eat and drink edible foods.

Foul waters and foul meats they’ll take, if they can get no better, but not poison.
_{The Return of the King - Book VI, Chapter 1: The Tower of Cirith Ungol}

The water was still worth fearing, as noted by Faramir and the caution exercised by Sam

Sam sprang towards it. ‘If ever I see the Lady again, I will tell her!’ he cried. ‘Light and now water!’ Then he stopped. ‘Let me drink first Mr. Frodo,’ he said.
‘All right, but there’s room enough for two.’
‘I didn’t mean that,’ said Sam. ‘I mean: if it’s poisonous, or something that will show its badness quick, well, better me than you, master, if you understand me.’
_{The Return of the King - Book VI, Chapter 2: The Land of Shadow}

---

Outside Gorgoroth

While Gorgoroth was consistently described (as above) to have a foul air, filled with reeking smokes, the rest of Mordor and especially the fields around the Nurn were certainly cleaner, and able to grow crops (where the food was produced for Mordor's armies)

Neither he nor Frodo knew anything of the great slave-worked fields away south in this wide realm, beyond the fumes of the Mountain by the dark sad waters of Lake Núrnen; nor of the great roads that ran away east and south to tributary lands, from which the soldiers of the Tower brought long waggon-trains of goods and booty and fresh slaves.
_{The Return of the King - Book VI, Chapter 2: The Land of Shadow}

---

Differences

It is worth noting that the passage occurs very differently in the books. While the Council of Elrond largely followed the same theme, in the film Boromir was portrayed to be far more desperate. Attempting to thwart any suggestion the Ring be taken to Mordor so that he make take the Ring to the defence of Gondor. In the films, this was necessary for two reasons. The first, to build this great mystery around the land of Mordor in the first two films before revealing its horrors in the third. The second, to emphasise the desperate state Gondor is in.

In the books, Boromir cares only to aid the defence of Gondor, although any suggestions from the wise that this isn't possible is accepted, not rejected. Note in the below extract that all Boromir's pleas are to protect the free people's of Middle-earth, never does he try and persuade them of the horrors of Mordor.

'None here can do so,' said Elrond gravely. 'At least none can foretell what will come to pass, if we take this road or that. But it seems to me now clear which is the road that we must take. The westward road seems easiest. Therefore it must be shunned. It will be watched. Too often the Elves have fled that way. Now at this last we must take a hard road, a road unforeseen. There lies our hope, if hope it be. To walk into peril-to Mordor. We must send the Ring to the Fire.'
... Boromir stirred, and Frodo looked at him. He was fingering his great horn and frowning. At length he spoke.
'I do not understand all this,' he said. 'Saruman is a traitor, but did he not have a glimpse of wisdom? Why do you speak ever of hiding and destroying? Why should we not think that the Great Ring has come into our hands to serve us in the very hour of need? Wielding it the Free Lords of the Free may surely defeat the Enemy. That is what he most fears, I deem.
'The Men of Gondor are valiant, and they will never submit; but they may be beaten down. Valour needs first strength, and then a weapon. Let the Ring be your weapon, if it has such power as you say. Take it and go forth to victory!'
_{The Fellowship of the Ring - Book II, Chapter 2: The Council of Elrond}

The closest we get to a similar statement, comes from Faramir warning the Hobbits of the waters in the Morgul Vale.

'May no hunger trouble you on the road,' said Faramir. 'You have little provision, but some small store of food fit for travellers I have ordered to be stowed in your packs. You will have no lack of water as you walk in Ithilien, but do not drink of any stream that flows from Imlad Morgul, the Valley of Living Death.
_{The Two Towers - Book IV, Chapter 7: Journey to the Cross-roads}