As a general rule, Microsoft doesn't care about personal problems, and sending messages containing illegal information is something I'd advise against online no matter the communication method. I wouldn't worry at all unless you make a habit of frequently discussing illegal activities.
Yeah from what ive seen its just the same tech they used in live messenger and for bing. Which scans for phising, spam and dodgy sites that can cause problem. Also the log said head if it was get then i would be worried. However it is stated within the t&c's of the service.