Although counsel is not supposed to mislead the court (e.g. by incorrectly stating evidence), the reality is, we all make mistakes and when there are so many facts at hand, oftentimes conflicting facts, innocent misstating of facts may sometimes occur. Lawyers are human and therefore, make mistakes. This is why we have two sides. The other side acts as a check and balance. Given the reality of things, not all misstating of facts will constitute miscarriage of justice.
Miscarriage of justice is when the court, after considering all the evidence and arguments, consider that a decision more favourable to the appealing party would have been issued had the error not been made. Hence, if the misstating of fact was so material to the determination that without the error, the appealing party would not have been convicted or would have been in a more favourable position, then there is miscarriage of justice and the appeal would be accepted.
Similarly, if a judge refuses to admit a particular piece of evidence, and this evidence should have been admitted under evidence law, and this evidence, if admitted, would have significantly changed the outcome of the case and the outcome would, in all probability, be more favourable to the defendant, then there is miscarriage of justice and the defendant should appeal on this ground. However, the defendant should have brought it up during the original trial and notified the judge of the procedural irregularity.