In SSP (Survival Singleplayer), the achievement "Diamonds to you", which will be taken if you throw diamonds at another player, can not be achieved, If you throw diamonds at yourself, it doesn't work (well, that, didn't surprise me). Haven't tested if it works if you throw a diamond at a zombie that can pick up stuff, but implementing that would be already a fix for this.

I'm kind of not sure if this is a suggestion or a bug, but for many player's it would be a goal to achieve all Achievements (especially with the improvements to them the last versions), and it would just bug them if they can't get that one without setting up LAN etc.

Another possibility would be to make this Achievement server-only.