You need to go thru the original transcript line by line, and highlight anything you said that you think is important, or anything the JP did/said that was incorrect and then you need to make those points known to the Judge at the appeal.
However, it is important for you to note the following:
- When the officer was on the witness stand, this is the "evidence" given by the prosecution. Any questions and comments that you brought up to the officer during cross-examination is not evidence in itself, but is simply trying to reduce the weight of the officers evidence.
- Did you take the witness stand yourself, or did you only cross-examine the officer? If you only cross-examined the officer and never took the witness stand yourself, then that means you did NOT enter evidence at all. If you did take to the witness stand, then this is your evidence.
So make sure you are making the right arguments about (1) bringing doubt to the officers testimony during cross-examination, and (2) the evidence you provided while on the witness stand.
The only case I can think of that may be helpful to you is this one:
R. v. Lifchus [1997] 3 SCR 320 http://canlii.ca/t/1fqzt
Here are a couple quotes:
"the standard of proof beyond a reasonable doubt is inextricably intertwined with the presumption of innocence, the basic premise which is fundamental to all criminal trials, and that the burden of proof rests on the prosecution throughout the trial and never shifts to the accused."
"A reasonable doubt is a doubt based on reason and common sense which must logically be derived from the evidence or absence of evidence. While more is required than proof that the accused is probably guilty, a reasonable doubt does not involve proof to an absolute certainty."
"Even if you believe the accused is probably guilty or likely guilty, that is not sufficient. In those circumstances you must give the benefit of the doubt to the accused and acquit because the Crown has failed to satisfy you of the guilt of the accused beyond a reasonable doubt."
The other thing you may want to also bring up during your appeal is that the JP had a Reasonable Apprehension Of Bias.
"Reasonable Apprehension of Bias"  A reasonable apprehension of bias is the standard by which a judge or
decision maker can be removed. Bias is a predisposition to rule in favour of one side to the detriment of the other. The bias can be real or perceived.
Justice de Grandpr© explained the test for reasonable apprehension of bias in his dissenting reasons in Liberty v. National Energy Board, [1978] 1 S.C.R. 369, at p. 394:
[T]he apprehension of bias must be a reasonable one held by reasonable and right minded persons, applying themselves to the question and obtaining thereon the required information. ... [T]hat test is "what would an informed person, viewing the matter realistically and practically – and having thought the matter through – conclude. Would he think that it is more likely than not that [the judge], whether consciously or unconsciously, would not decide fairly."
Related Cases:
Baker v. Canada (Ministry of Citizenship and Immigration), [1999] 2 S.C.R. 817
Wewaykum Indian Band v. Canada, [2003] 2 S.C.R. 259
Toronto (City) v. Mangov, 2014 ONCJ 351 (CanLII)
"A reasonable person could interpret the courts comments as indicating a predisposed attitude towards conviction when it came to a speeding trial."