An interesting challenge for you Burr, and easy for a boss to ask for but less so to make happen. Miles has mentioned some metrics - as he says, some good, others not so. Several of the ones he mentions are a bit reactive - things only get counted after they've gone wrong, and meetings etc. are only of value if they achieve something positive. But he's quite right, they get used, probably because they're easy to count!
Maybe more pro-active measures might be numbers of recommendations from surveys (we do 'safety surveys' in the the ATC world although there's little common agreement on what they are). Often more interesting - if you've got enough data - are the trends.
I've seen good - and easily visible - results from analysis of occurrence reports where severity of events could be seen to move from serious to less serious classification and a quick survey pretty much confirmed that increased awareness and better adherence to procedures (promoted by safety the people) contributed to the improvement.
Unfortunately the only good indicators that I've come across need analysis and often are compound indicators which draw conclusions from several sources of raw data - just counting chickens/events only tells you how many chickens or events you have. Show an improving trend and there is often doubt whether it's real or under-reporting or people have found a way to fool the system.
One thing that I have seen is that financial incentives don't motivate people for long - and the amounts involved where I have seen it used were not great. Recognition seems to be a greater motivator if used in the right way - 'Employee of the month' sort of thing. Got any tame psychologists who can advise?
HTH, a bit anyways.