I can't see any ! ...... It's a very specialised factor of the court process, any barrister can, and almost always does , say , right in front of the court, as loudly as possible, ' my client will of course be appealing'... but the actual program of that requires a lot more than a tantrum because I've been found guilty.
Dawson will have to come up with verifiable, tangible new evidence, nothing from his fortune teller, or his star sign, or what the tea leaves say. Cold , hard, new evidence that the prosecutor agrees to.
The other chance is, Dawson will have to reveal, expose , highlight a verifiable and tangible error that the judge has made in conducing the case over all, in instructions to the jurors ( none in this case ) in directions to the barristers, etc. In admittance of an evidence, ...
Harrisons summing up was detailed to a remarkable degree, as most if not all summing ups of a judge only trial are, which is why they are pure pleasure to those who love a good tort. Not a word is wasted and there is a real generosity in the painting for the public of the judges perception and conclusions.
For these reasons, I do not see Dawson being granted leave to Appeal, but on the other hand , he is entitled to ask the court, no doubt about that, and there is a small chance that Dawson may have kept back a tiny tiny bit of new evidence. Finding an error in the judges conclusions, no.. ..that is not going to happen, I think.