Dead groups that shouldn't be?

EDIT2: thank you, my question has been answered

This was my second game ever (I don’t count losing to the tutorial bot a game =P):

Play at first ended at move 71 (mutual pass). Then in removal of dead stones and territory counting phase, the system counted my groups at F4-G3 and J1-2 as dead when clearly white had no possible way to capture them.

We then continued to fill in the remaining gaps at H1, J5 and J3. The system then counted my groups as alive (as it should since they are now connected to my half of the board).

Was that just a system error or was there really some way white could have killed my groups that I’m not seeing?

EDIT: please don’t mind my self annotations, just recording what I was thinking at the time

The scoring system sometimes makes mistakes in determining life/death status of stones. These mistakes have to be manually corrected by the players during scoring.

No, there was no way for white to capture those stones, unless you completely ignored the threat at H1.

At the end of the game, after the first set of passes, H1 was an unfilled dame (http://senseis.xmp.net/?Dame) that does not really affect the score, except to force black to play at J3 to fix the teire (http://senseis.xmp.net/?Teire).

Formally, instead of passing the first time, white should have played at H1, then black should play at J3, and then the game should have ended. However, it’s also not uncommon to see players to just end the game with those two points unfilled, but then mark J3 as not territory during scoring.

It was not necessary to fill in J5. This only reduced a point from black’s score, as it should have been counted as territory.

Thank you for the explanation. More theoretical than what was explained to me in the review but means the same thing.

I should probably stick to formally finishing games first before taking shortcuts (like this case), in case of misread.