I think having a dedicated safety person is always a postive thing, if it is the right person with the right skills, the right commitment and the right set of morals. Companies without one often rely on front line supervisors who are typically ill equipped and educated to do safety the way it needs to be done, they may also give into production demands in ways that a safety person would not.

As far as health and safety issues go in the UK, Each employee of a company is responsible for any H&S related issues and risk assessment of a situation.
This approach helps to look after others wellbeing and also look after the company should any accidents arise that could have been avoided with the vigilance of the employee.
However, Most company managers etc tend to turn a blind eye and show contempt towards employees that try to work with H&S legistlation that costs the company money.
This attitude makes it hard for anyone to adhere to H&S issues without being labled a trouble maker or someone that is not part of a team thus putting their jobs at risk should they push H&S related issues that the Management don't like.
Management love "YES" Men!
when an accident does arise, then they play the blame game and tend to look at the lower end of the ladder to place the blame.
100% of H&S is down to common sense and logic, If employees don't have either then it boggles the mind why they are employed in the first place.

Sometimes it is the dollar amount of a single accident (no injuries), rather than the number of accidents that motivates the company to go to great lenghts to attempt to punish.
Go Unions!

I guess that might motivate the other employees to be "more safe", especially if they know why the accident prone employee was let go, but can you safely let employees know why someone is terminated?
and I would far rather have a "positive (carrot) idea than a "stick" idea. I know of a company that has a drawing for a $100.00 gas card every other month when there is a very limited amount of reportable injuries in the previous period.

Our health and safety girl helps with compliance and writing up damage or incident reports.
One of her other jobs is to compile and present evidence to help in terminating employees involved in accidents. Look out.

In my not so humble opinion, it really does not matter what job title the person has, if they are more concerned that "he protects his job rather than" /what ever is in the best interest of the company/, then he is an anchor, and not helping paddle to get where they want to be.

I think there can be a perception among those saddled with that title that their job may well be to be the scape goat should/when the company has a real health and safety disaster, like a drunk employee drive a truck off the dock after the holiday party, or the place have to close down a few days because the parts department put shelves too close to the sprinkler system and the fire marshal was not be willing to wait for it to be fixed, with people doing business in that area or any of thousands of other possible disasters that can happen in our industry.

I would like to hear if anyone has any ideas how a "health and safety" man could motivate any other employee to consider being safer in their daily tasks.

One person is a bad idea ( unless it is a small company say under 75-100 people then it's normally handled by the Human Resources Department), something like this for larger companys is usually better in a commitee enviroment where different ideas and situations can be handled.
It also prevents a company getting into an issue like you are talking about.
Most companys here in the States have Enviromental,Health and Safety teams (1 employee & 1 manager from each branch) that meet every 3 to 4 months to not only review past safety issues but be able to prevent future accidents and long term health issues not related to on the job injuries.
They also discuss seperate issues at each branch and how it is being corrected.
They in turn report to the area Company Presidents, and in all the years I have been with the company I don't remember them ever turning down a safety recommendation or a request by any employee that felt their life,health or safety was in danger.
In our company anyone from the President down to the newest tech who was just hired can stop any operation or activity if they deem it unsafe.
Each of our branches have assigned Safety persons who are trained in emergency first aid, CPR and fire fighting, then all of the employees go through different safety training through out the year. When you have 1700+ employees in 12 States safety doesn't cost, safety pays.