[The Saucepan Man]

But Sauce, the debate scene was before Frodo's betrayal of Smeagol to Faramir. The point of the Cirith Ungol scene in the book was that it was Smeagol's last chance. (Eomer)

Fine. All I am saying is that the debate scene in TTT suggests that Smeagol might have been able to repent. But then he sees himself as having been betrayed by Frodo at Henneth Annun, and the chance is lost. In the films, that is Smeagol's last chance.

While it’s not portrayed in the movies, at least not explicitly, Sam’s mistreatment of Gollum/Sméagol is shown an awful lot in the movie. (Knight)

Yes, but I think that Sam's attitude towards Gollum in the films is something which the audience can understand and relate to. Certainly, it is not sufficient to turn the audience against him. It is not Sam's attitude that turns Smeagol away from repentance. Smeagol's repentance, in the films, is lost by Frodo's (understandable) actions at the Forbidden Pool. Ironically, this is because Frodo is showing him mercy, in that he is trying to save Smeagol from death. Does this weaken the value of Frodo's mercy? I don't think so because, if Frodo had not shown him mercy at Henneth Annun, Gollum would not have been present at Sammath Naur and the Ring would not have been destroyed. And there is a certain tragedy in that. Frodo's mercy loses Smeagol his last chance at repentance (in the films), but nevertheless preserves the circumstances necessary for the destruction of the Ring.

If PJ hadn’t wanted to show Gollum’s good side, then he wouldn’t have inserted the debate between Sméagol and Gollum, or Gollum’s recognition of his own name when spoken by Frodo, or even the prologue for RotK which highlighted Gollum’s once decent past. (Knight)

The debate and Gollum's recognition of his name were both in TTT. As I said, I think that Jackson did want him to be a sympathetic character in that film. The prologue to RotK is interesting. I think that it was a good addition. We see Smeagol in his pre-Ring state, and so can feel appreciate the tragedy of his fall (as a result of coming into contact with the Ring). But, at the same time, we can see that, having not even touched the Ring, he was driven to murder his best friend for it. I think that this sets up nicely his role as an out and out villain in RotK. It also heightens our appreciation of Frodo, since the contrast with the Ring's effect on Smeagol (and also Boromir) puts Frodo's torment, and his strength in resisiting its influence for so long, into context.

What if Gollum had repented then and there? I know it’s been asked before what would have happened if Gollum had repented before, but would Sam and Frodo have made it through to Mordor after all? (Knight)

Tolkien does speculate on this in one of his Letters (No 246). He says:

Sam could hardly have acted differently ... If he had, what could then have happened? The course of the entry into Mordor and the struggle to reach Mount Doom would have been different, and so would the ending. The interest would have shifted to Gollum, I think, and the battle that would have gone on between his repentance and his new love on one side and the Ring. Though the love would have been strengthened daily it could not have wrested mastery from the Ring. I think that in some queer twisted pitiable way Gollum would have tried (not maybe with conscious design) to satisfy both. Certainly at some point not long before the end he would have stolen the Ring or taken it by violence (as he does in the actual Tale). But 'possession' satisfied, I think he would then have sacrificed himself for Frodo's sake and have voluntarily cast himself into the fiery abyss.

I have to admit that I have a problem with the final sentence, because if (as Tolkien also tells us) no one could voluntarily have destroyed the Ring, then I have difficulty understanding how Gollum would have been able to throw himself into the fire, since that would inevitably have involved the detruction of the Ring. For me, it seems more likely that Gollum would have accompanied them to Mount Doom and then, driven by the irresistable call of the Ring, attacked Frodo for it. The ending would then have been much the same, save that we may not have witnessed Frodo's final 'failure'.

But that is perhaps an issue for discussion elsewhere (and there are topics on this already).