HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

I don't understand this phrase. What does "invalid type" mean? Does it mean you can't play as a dungeon? You could before, but you can't in this save. It's a mystery.

Yes, it's a mystery, but honestly, I can't imagine how HD could be involved. I'd really like to figure it out, but unfortunately, I can't reproduce all these terrible things myself.
Yes, with the bug orange save.GM2, I was mistaken.
I looked at the save with Pikedram - if you press replay after hiring any hero, the game crashes. The direct cause: the replay tries to set the focus on the hired hero (who hasn't been hired yet in the replayable turn) with invalid coordinates for the hero's focus: -1;-1;-1
Why this happens - who knows.
I don't even see a reason to try to fix these saves, because their flaws, unlike the splits/silvering, are not typical and I encountered them for the first time.

In the next version, I will make optional game dump generation, which can be done when such glitches appear; maybe this will help me figure out what's going on.