I've used a system called Synergi that would meet your requirements, aside risk assessments. It has the capacity to store them electronically and set review dates once you assign a case number to it. The interfaces are good between incidents / inspections / audits, but its a case of setting it up exactly how you want and ensuring consistency of data entered. HTH. Oh, I have no affiliation to this system other than a user.

I used to work with Target 100 that could do all the things you ask for. It was quite scalable as well, from simple paperwork forms through to complex user reports on audits and accidents stats. It was up to the user how far they went down the completely electronic route. Also had software for use on PDAs. Again, no affiliation with them and no idea of the costs involved these days but they do offer free trials (from a quick check on their website just now).