Vegemite beyond expiry date?
Best-before dates aren't the same as use-by dates. Whilst you shouldn't consume a product after it's use-by date, best-before dates are more about quality than safety. Basically, after the best-before date, the product may start to deteriorate in terms of flavour, but that doesn't mean you can't still eat it.

I'd expect that the salt content of Vegemite would keep it sound for a long time. I've certainly had half-eaten jars of Marmite (sorry, I'm a Marmite guy, not Vegemite) kicking around in the pantry for way longer than they ought, and they've been just fine. 

Butter and breadcrumbs from the knife may well develop mould if they're left in the jar for a while, but that would normally just be on the surface and easily removed. Much better to remove crumbs before they get to that stage - or, easier, just use a clean knife.