I have the exact same question... 'martedì notte' doesn't sound very correct to me!
Actually it sounds more natural to say "martedì notte" than "la notte di martedì". It's a a time expression and works other parts of the time: "domenica mattina", giovedì pomeriggio", "sabato sera". It's the same in English, if you think about it :-)
that makes sense... my mother language is portuguese, and we don't use that expression. I thought that italian would use the same expression we do ('notte di martedì'/'noite de terça'), when actually it's a bit more like english. well, now I know :)
'Evening' and 'night' in English do not correspond exactly to 'sera' and 'notte' in Italian. For example, in much of Italy, one would greet someone with 'buona sera' anytime after lunch until late at night. 'Buona notte' is generally used only when you are leaving or going to bed. I think it is appropriate for DL to accept both 'sera' and 'notte' for the English 'night.'