Yes, what Cannon wrote in her dismissal of the case was that Jack Smith was improperly appointed. That comes from an amicus brief written by the Federalist Society suggesting that a president must appoint a special counsel and that Congress has to approve the budget for the special counsel, otherwise he is not validly appointed. Justice Thomas wrote his own little special opinion he attached to the immunity decision that was all about making sure this idea was there. Essentially, the opinion Thomas attached to the decision, which you are correct no other justice signed on to nor agreed with, was a letter to Judge Cannon basically asking her to throw out the documents case. Trump's lawyers submitted the Thomas opinion to her in full, and she cited it in her dismissal several times. 

So, that is the basis for her dismissal. Yes, the problem with it is, it is not just weak sauce, it is based on no law and no guidelines set forth for the appointment of a special counsel. Which, state that the AG has the power to appoint a special counsel at his discretion. No, the president is not involved and no Congress does not have to sign off on it by approving the special counsel's budget. That is essentially made-up. I'm not sure what they based it on, but there is a simple two paragraph set of rules for a special counsel appointment, and there is nothing in it about Congress nor the president. 

If this were the case, when Trump was president, Robert Mueller was inappropriately appointed by Deputy AG Rod Rosenstein and they could have had Mueller thrown out as well through a claim that he was not a valid appointment. Of course, that did not happen. The AG and Justice Department can appoint special counsels, with no approvals by Congress or the president. 

So, yes, we have a nonsensical claim based on no law. However, I think this attempt is basically just Cannon's final delay in the case and it should stop the case in its tracks until sometime in 2025. Mainly because if the what Cannon did is found to be a joke by the 11th Circuit, Trump will appeal again to the Supreme Court. That should be a delay into 2025. 

Beyond that, only Thomas on the Supreme Court seems to have signed on to this nonsense, but how do we know that the other 5 Republican appointed justices won't do the same when it gets to them? They seem to invent stuff now when the opportunity arises, twist all logic and bend all laws to suit whatever idea they think will help Trump. Also, after they slow walked the immunity decision until the very last day they could push it to, my bet would be if they end up taking this case, they will take their sweet time with it and push it as far out as they can. Essentially hoping Trump gets elected, he throws out all of Jack Smith's work, and there ends up being no need to rule on it. 

Plus, you know if Trump gets elected, Thomas can retire and we will get Supreme Court Justice Aileen Cannon, who will be according to Don, 'the greatest Supreme Court Justice in the history of this country."