When to call a judge came up several times during the worlds livestream and made me realize that there's a lot of disagreement on best practices/etiquette. FFG tournament rules describe judges:
When a judge is observing a game or an issue is brought to his or her attention, the judge should inform players when they are not following the game rules. Players have an initial opportunity to resolve any situation among themselves, but any player may alternatively ask the judge to make a ruling
Worlds 2017 had several game losses due to mistakes like flipping over a stack all at once for Information Sifting or running after playing Peace in Our Time. The question is what to do if this happens in one of your games.
If you recognize an illegal game state that cannot be perfectly reversed, I think you should call a judge. Perfectly reversed means that no new information was gained, including the information that the other player intends on passing a relevant action window. For example, if the runner forgets to collect credits from Daily Casts before using a click on Magnum Opus, that's easy for both players to agree to resolve the mandatory trigger. You could call a judge if you're not sure, but it's not really needed in that situation in my opinion. Another example is remembering after a Maker's Eye that Peace in Our Time was the runner's first click, disallowing a run. New information would be if the corp decides to rez or not, or obviously if the runner sees cards off R&D. This should definitely be a judge call. At a worlds-level event, this would also likely be a game loss.
Nobody likes to win on a technicality--especially against someone you know--but you shouldn't be afraid to call a judge in this situation, that's what judges are for. It's unfair for the other player to pressure you into resolving it without a judge or think you're a jerk for calling one. There should be no stigma involved in calling a judge, especially not at the highest level of competition. Calling a judge does not mean you're accusing the other player of cheating or trying to get a free win and it doesn't make you a jerk.
A notable magic site just published a relevant article from a top-level player that provides an insightful viewpoint:
I'm interested to hear other people's ideas on judge etiquette and alternative perspectives.