Learn Italian: Il tetto è rotto; oltretutto, c'è muffa che rovina le pareti. - The roof is broken; besides, there is mold that ruins the walls.

Yes, but it changes the tone slightly. inoltre is a neutral "furthermore" or "additionally." oltretutto carries the sense of "on top of all that" or "to make matters worse." Because we are piling on bad news (a broken roof, plus mold), oltretutto is the perfect connector for this negative escalation.

Why does the sentence use le pareti for "the walls" instead of i muri?

le pareti specifically refers to the interior walls of a room. i muri is a broader term used for exterior, heavy, structural walls, or standalone outdoor walls (like a brick wall in a garden). Since mold typically ruins the inside surfaces of a house, le pareti is the most precise choice.

Why is there no article or partitive (like della) before muffa?

When stating the general existence or appearance of an uncountable substance, Italian can drop the article entirely, just like English ("there is mold"). You could absolutely say c'è della muffa (there is some mold), but stating just c'è muffa effectively emphasizes the raw fact of the problem.

Is the semicolon and comma punctuation around oltretutto strictly necessary?

Yes, when using connectors like oltretutto, inoltre, or per di più to transition between two full independent clauses, this is the standard punctuation. The semicolon (or a full stop) separates the two complete thoughts, and the comma after the connector forces a pause that highlights the escalation of your argument.