Hey!
This is a good idea! Share buttons should be reviewed to match the audience and business aims. Ridding the site of low-value or rarely used buttons could also help with performance and user experience. Quality over quantity!

The same goes for outbound links. Check them periodically and make sure they still lead to the intended site or page--and that the content is still worth linking to.

The same goes for outbound links.

Easier said than done when you have 20 year old forum. It's been a few years but I'm due for cleanup. Last time I first extracted just the domains. Then another script that would grab screenshot through web browser with the filename being the domain. Browse the six gazillion thumbnails to find the bad domains.

What I really wish I had was built in validation for outgoing links. e.g permanently whitelist, permanently block and third category where it would require re validation down the road.

>> due for cleanup

There are link-checking tools available that will spider your site and report back on problems which you can then fix, one by one. 404s, expired sites, weird redirects, that sort of thing, also specific content that you want to look for. For example, watch for words which suggest that a link has turned into gambling or #*$!.

If your site is large, check a section at a time. Staying ahead of link rot is an ongoing task, but the effort is good for your users and certainly won't hurt your SEO. To be 100% free from bad links is unlikely for a site like yours, but you can certainly achieve some improvement.