Not sure whether im worried or not...
Without knowing the details of the first case, i must say it does sound extremely worrying. A chat between two people should be private no matter how it is undertaken. If it is then published online at a later date by one of the parties then perhaps, very perhaps, there may be a case to answer for if the message was threatening, but then i would have to say both parties (definitely the poster) might be in trouble. And it should definitely not fall under the auspices of the obscene publications act, that it does in this case is just ridiculous. E.g if it was a conversation about raping someone (even if no specific name was mentioned) then perhaps it could be breaking some sort of stalking or threatening messages law but definitely not the obscene publications act!
The second case, though i have less trouble with. If you ring through a bomb threat, you can expect to be chased up and charged with making a threatening call. If you tweet the bomb threat, i see no reason why this should be handled differently. However, in this specific case, its gone to the extreme because this is obviously not a serious threat. At most it should be counted on about par with making a fake police or 112 call. That its gone to this level is again frankly ridiculous!