Is there anything official how judges should handle forgotten "must"-effects like taking credits for compromised employee? Only remind the players to ensure a correct game state in the future or shall we "correct" the current situation (give the runner one credit)?

Does it depend on if the game state was changed significantly or not i.e. if decisions were made in regard to the credit pool of the runner (rezzed ICE or Traces)?

First, you should always ask the other player if you can take to forgotten action/credit/effect, mandatory or not. It will generally work if it was not some turns ago, or if it is a small mistake.

There is nothing "official" about "must happen" effects, but if you ask a judge (and the answer will be the same in most games) he will answer : "You have to take care of your own cards/effetcs..." or "sorry, you missed the opportinuty to..."

We learn a lot from our own mistakes

What if the missed opportunity was a disadvantage of the controlling player i.e. the tags for joshua? I thinkg as judge I should give a penalty but is a warning enough in this case especially if the situation happens repeatedly?

In that case you are right. There is a thin line forgotting something and cheating.

If it happens one time, just warn the player; But if the situation happens repeatedly, you can directly call the judge.

No pity for cheaters.

Based on my experience with other card games, the standard way of handling it is If someone is forgetting something that benefits them, if it's still the same turn you should allow them to do it (such as collecting credits from a Campaign), though if you did a run based on them having X credits but they announce they actually are supposed to have a load more, then tough on them.

If someone is forgetting something that hinders them, such as Joshua, call a Judge. He'll likely issue a warning, and that'll be that. The reason you call a Judge is because otherwise this person could be doing it in every game, and often getting away with it. The warning means the Judge knows that if it comes up again it's active cheating, rather than a simple mistake.

As a judge, it's my philosophy that BOTH players are responsible for maintaining a correct board state. If someone forgets a credit and the game state hasn't relied on that sort of thing, I'll let the player correct the state and issue both players a warning. If it happens repeatedly (say, more than twice), I'll issue a game loss for either the player who is advantaged by the forgetting.