On the threshold for investigation, there are maybe three parts to your question, as I understand it.
In terms of investigation, I must stress that these are penal investigations. They have to meet the standards of criminal law in terms of fairness, due process, and the various fundamental rights that are provided by the charter. Of course there's the burden of evidence, which is beyond reasonable doubt.
In terms of challenging election results, this is a matter for the court. Any elector can bring a matter before the court to ask for the annulment or contest the result of an election as long as it is within 30 days of when the elector became aware of the facts or reasons for disputing the election. The elector has to determine or show that the results were affected by the circumstances being brought before the court.