If it is provable that I was charged (assume 2000$) for services/products I didn't buy, would law enforcement have enough time to look into my case?
If you are charged because another person fraudulently used your card or the business is involved in the fraud, you may file a police report. However, the clearance rates for small-amount thefts and frauds are fairly low in Canada.
If it is purely an unintentional software error on the part of merchant, the police will not get involved. It is a civil case, not a matter of criminal law.
You can file a lawsuit against the merchant and your bank but this is rarely necessary to resolve this type of issues.
To alleviate your fears and encourage use of credit cards, payment networks (Visa/Mastercard/Amex/etc.) usually require stronger consumer protection process as a condition for banks and merchants to participate in the network.
You are also protected by law against unauthorized credit card charges.
Unauthorized credit card transaction
When an unauthorized transaction is made with your credit card, your maximum liability, by law, can't be more than $50.00. Your credit card agreement must explain your maximum liability if your card is used without your permission.
Visa, Mastercard, American Express and Interac have committed to protect you against financial loss if your credit or debit card is used without your permission. According to this public commitment, you will not be held responsible for the unauthorized transactions and won't have to pay any fee.
Learn more about these commitments and policies. (Link to policies of payment networks and your rights under law and relevant agreements)
If you were charged fraudulently, the first thing and usually the only thing you need to try is the dispute process by your bank. The bank decides on the merits of your claim, and they usually favour the consumer. If the merchant disputes your dispute, a police report might be needed to convince the bank if there is an actual fraud involved.
If your dispute is successful, for credit cards, it is usually credited back to your account in a few days or within the next billing cycle.
Will judge have enough time to hear my case?
If your bank and the merchant refuse to refund you, you may bring a claim before a competent court. Usually for 2000$, it would be in a small claims court with simplified procedures. Judges do hear these cases. In many if not most cases, a settlement is made before trial. In some jurisdictions (e.g. Ontario), a mediation-like settlement conference, led by a deputy judge, is mandatory before going to trial. The deputy judge usually makes some preliminary comments on the strengths and weaknesses on each party's claims/defences and many people choose to withdraw or settle at this stage.
Before COVID, this usually takes within a few months after a claim is served to the defendant and the defendant files a defence.
If the defendant ignores the claim, you usually get a default judgement in favour of you.
If you win in court, an order to pay is issued against the defendant and if it is not paid in time, you can apply to the court to enforce the order by e.g. garnishment or seizure.