Looking at possible grounds for appeal for a moment, I note that Depp's lawyers imply that NGN have been allowed to cherry pick the evidence. I've been looking at the judgement and previous judgements in this case with that in mind to see what I could find.
The judge excluded one of Depp's witnesses on the basis that their evidence was irrelevant. Depp may try to argue that this witness should have been allowed, although I'm not convinced he would succeed.
The judge heavily edited the witness statement of one of Depp's other witnesses, removing a substantial portion of it. Depp may try to argue that this witnesses statement should have stood unaltered. I haven't seen the unedited statement so can't comment.
The judge refused Depp's application to force Heard to disclose evidence (documents, photographs and recordings) that his lawyers clearly believed would help his case. They may argue that this evidence should have been disclosed and that, had this happened, it would have undermined NGN's case.
The judge refused to allow Depp to call expert witnesses. Given that there are a number of places in the judgement where the judge refuses to make findings on the basis that there was no expert evidence, I suspect Depp's lawyers will argue that the expert evidence should have been admitted and that this would have forced the judge to make findings in Depp's favour on these matters which would have undermined his judgement. Of course, if Depp's experts had been admitted it is possible NGN would have introduced their own experts so it is by no means certain that the expert evidence would have changed things.
This is all conjecture on my part. I have no inside knowledge.