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I don't know the rule with 'this' and 'that' but saying 'that' may be more precise in reference to the specified time/date/thing. Could be totally wrong though: http://dictionary.cambridge.org/grammar/british-grammar/this-that-these-those
This/that/next weekend is tricky even for native speakers though. Many arguments have ensued due to the varying interpretation of 'next weekend'? Do they mean the immediately coming weekend, or the weekend after? It varies so don't worry too much (but do be aware of it!)
I know, by this evening I meant the evening mentioned in the first post :)
Is there a rule saying that in this kind of case "this evening" means "the current evening" rather than "the evening that was mentioned before"? I got corrected in the same way about "this weekend" yesterday.