As I understand ITIL Service Management, Problem Management is a process underneath the Service Operation lifecycle phase. The objective of problem management is to prevent problems, minimize the impact of problems that *do* happen and eliminate recurrence.

As far as goals...I think it depends on the state your problem management effort was in before. I am a fan of smaller incremental goals when trying to change the fundamental way a thing is approached. This allows for a feeling of success to happen soon enough to calm fears of the unknown.

So, for a new effort, I would say getting a problem tracking system in place and a known issues list started (along with a known workarounds list) are good goals to start with. These are a first goal for me because they allow you to clearly identify the existing problem areas and gather useful metrics about how many problems are actually occurring (rather than using anecdotal evidence). This in turn gives you facts to use to justify costs associated with beefing up your efforts...or determine you are already doing ok.

Ultimately though, the big goal is to transition to being proactive in problem management and identifying root causes. Getting to a place where you have sufficient monitoring and analysis efforts in place so that most problems are identified *before* they impact the business. You can never expect to stop 100% of issues before they happen, so the definition of what "most" means is really organization dependent. There comes a point where the cost of identifying problems of certain types is more than the impact they would have if they happened, so your organization would need to determine where the sweet spot is.

Since, in ITIL, Problem Management is a part of a larger framework, another goal (assuming you are implementing other areas of the framework) would be the pervasive use of the new terminology. All reports, emails, etc, using the correct terms. One of the hardest parts about ITIL is getting people to use the right name for what they are talking about.

Disclaimer: I am not ITIL certified. My knowledge of ITIL is from being part of the effort at a large company.