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In the phrase dem alten Hafenviertel, I have dem which is dativ of der or das, then I have alten which I suppose is the accusative of der and, at the end, I have the noun Hafenviertel which has the member das.
Can someone explain to me how is this construction is even valid?
-en at the end of an adjective doesn't imply it's accusative. There's lot of -en not concerning Akk.
See schwache Deklination in this table.
Dem alten Hafenviertel
is purely Dative. Addressing the last question, strictly speaking, that construction is valid because it's the only possible correct construction.
But that doesn't really help. Maybe what you want to know is the following. Given a chain of a determiner (see link bellow), an adjective and a noun:
Det.AdjNomen
you might want to know, which ending does the adjective bear?
First choose according to this table the type of declension your determiner induces: you have three options, namely, strong, weak and mixed. (in your example, it was das – as you stated). Then GOTO the inflection table itself and, first according to whether you have strong, weak or mixed, pick a table (in your case, weak declension). Then pick your entry according to the gender and case (in your example, neutr. and dative, signaled with stars bellow; little arrows point to the right ending).
Schwache Flexion (mit bestimmtem Artikel)
Maskulin Neutrum* Feminin Plural
Nominativ der alte das alte die alte die alten
Akkusativ den alten das alte die alte die alten
Dativ* dem alten →dem alten← der alten den alten
Genitiv des alten des alten der alten der alten
Accusative wouldn't use an -n ending:
Die Zeitungen schreiben viel über das alte Hafenviertel.
No alten used at all here in the accusative case.
