I was very sad to see Paloma go, because I liked her (and really don't understand the hostility to her on here) but I think she did deserve to be fired, though not for the reason Sugar gave.
There's no doubt that Paloma, in her desperation to stay in the process, is prone to getting carried away in the boardroom. She did that even with Shibby, though he was so bad that her scorn was really not much misplaced. However, she wildly exaggerated Alex's failings on this task - he was a bit annoying, but nearly so bad as she implied. However, I think this arose because she wanted to win so passionately, and that passion has often commended itself to Sugar in the past. Katie's rant against Adam in series 3was far worse than anything Paloma said, yet she escaped firing and nearly made the final.
Nor do I think Paloma made much of a mistake in who she brought into the boardroom. There's no doubt that Alex screwed up over the promotional stand; he himself admitted it. For me, his brilliant idea of getting an advert on the mall's TV was worth more than any promotional stand, though, and more than atoned for his error. Nonetheless, he did screw up, and from what we were told of individual sales didn't sell very well. It was fair to bring him in. As for Sandeesh, it may have seemed odd to bring her in after praising her, but then Paloma was clear that she thought everyone except Alex had been fantastic and was obviously torn over who to take in. Taking in Sandeesh because of her poor performance on earlier tasks may have annoyed Sugar, who saw it as an attempt to usurp his job, but I thought it was a fair criteria to use.
No, the real reason why it was right to fire Paloma is because of her main error on the task itself; product selection. Ultimately, this, not the promotional stand, is what lost the task. Losing Liquorice was a misfortune, and this was down to Paloma, Sandeesh and Chris, who failed to realise that they needed to enthuse more (there were signals from the Liquorice people that they should have picked up on). I felt it was a bit of a shame, really; the three of them were perfectly civil and businesslike, and weren't nearly as bad as Kirsty on the art task on Junior Apprentice (at least they looked at the clothes). I think that was a forgiveable error. However, Paloma made a big mistake in picking what even I could see was a range of clothes that wouldn't have general appeal. There were other clothes that the other half of the team had looked at and were enthusiastic about, and they would have been a much better choice, I thought.