Will I have problems entering a country if I have a cancelled departure stamp from my home country?
Will immigration ask questions about it, and what should I do?
Given that many countries don't supply departure stamps at all, and certainly not for citizens, I'd seriously doubt many customs officials are going to bother checking them all. Mostly they just glance through to see if any places you've been are on the watchlist, whether your name comes up on a criminal records search, and (if applicable) whether your visa is valid.
Used to have a passport with an arrival stamp but no departure stamp, official on departure had forgotten to stamp it. Never caused any trouble elsewhere (though my dad had something similar in the US and it raised a few eyebrows, but that was in combination with a smudged text on his visa, embassy worker had closed the passport before the ink had properly dried).
Of course if there's something raising a red flag and they do dig deeper, they might ask a question or two about inconsistencies like that.