What can I do to make sure it won't happen? Who is the right person to report this to? (apparently, the police can't make sure that it won't be used for identity theft)
You want to contact any one of the credit bureaus and put a fraud alert on your account. Once you contact one, they automatically contact the other bureaus for you.
As part of this, they should send you a credit report. Review it carefully and note any items that are not yours. You'll then need to dispute any items that are a result of this identity theft. You may be required to file a police report regarding the stolen identity, but if you filed one for your stolen wallet, that may be sufficient.
If the person who stole your wallet wants to steal your identity, it may be months before it shows up on your credit report. Make it a practice to regularly check your credit reports.
How do I check at any given time whether my identity was stolen?
Unfortunately, there is no easy way to check if your identity was stolen. The most common way is to check your credit report, but that only checks things that are reported to the credit reporting bureaus. If they use your information to start an account with a utility company at a rental house that typically won't go on your credit report until they are substantially delinquent. If they use your information to check into a hospital, that information typically won't show up on your credit report until the hospital sends the bill to collections.
I've had a case where the identity theft happened at Chase, but was never reported on my credit. So my credit report was clear, but Chase disallowed me from banking with them because the identity thief had delinquent accounts with Chase that for whatever reason were not reported to the bureaus.
How likely is it that it will be used in any form of identity theft?
My gut feeling is that someone who snatches a wallet and immediately runs up the credit cards isn't looking to steal identities, but rather for a quick score. I don't know if there are statistics that back up my hunch.