real_tzs, the answer to your question is very simple:
When you're logged in, the 'missing moves' have been happened due to someone who copy/pasted them in his post(s), directly from the Moves/Details box. That doesn't happened in the Public Comments(Or when you're logged out) because someone haven't made it, or copy/pasted the entire page into a comment(yet).
Sadly, this is very common to happen in public games, since the majority of players are just trolls/patzers who aren't paying much attention to the game, and just want to have 'fun' at other's expense. Note that high-rated players/players who really want to learn chess rarely/never would do these bad actions previously mentioned.
One of my vote chess games is not displaying all of the other team's moves. It is fine if I view the move list while not being logged in. If I view while logged in, then moves are missing.
Here's a screenshot of viewing the game while not logged in:
Here is the same game, viewed when I'm logged in:
This is not a browser issue. The behavior is the same in Firefox, Chrome, and Safari.
This is only happening in that one game. I am playing in two other vote chess games, and they are currently displaying fine when I'm logged in.