The first safeguard is for both counterparties in a transaction to confirm it if they have time verbally or via hand signals while in the pit before handing off their cards and carbon duplicates to a clerk who serves as a trade checker. Both trade checkers eventually find each other and confirm the transaction before time stamping and handing the cards off to the clearing firm to get the trades typed into the computer system. At the end of the trading day a preliminary run of the data entry is available to get checked by a trader or delegated to a clerk which is the final chance to catch a mistake before it hits the trading statement and becomes an outtrade to be dealt with before the market opens the next day.
Early each morning, outttrade sheets are left in an alphabitized stack outside the trading floor showing each clearing firm's and trader's outtrades which they have to resolve. To take advantage of being the first alphabetized listing (or in the old days when it was distributed to receive first delivery), one trading firm was named Aardvark because it's the first word in the dictionary.
The outtrade sheets would show price discrepancies, wrong clearing firm numbers, mismatch on buying/selling, trades which are coming into a trader which weren't picked up and trades going into another trader that they didn't pick up yet either. Most of the adjustments were just clerical as the previous safeguards kept from any unknown trades but in the past I've heard of errors which weren't discovered until this stage at a great cost. Generally if there were any honest errors a 50/50 split for upside/downside would be offered but I never had any issues as a trader or clerk so don't know how much that occurred.
As part of the official way to handle outtrades, a class from the exchange had to be attended to have it all be explained but in hindsight I can't recall one thing taught in it. After attending the class, the badge above was issued to note that a person was OTQ (Out Trade Qualified) but it was just a formality. Dealing w/outtrade clerks as part of early morning duties when I was clerking was always pretty simple as all the outtrade clerks were always competent and they knew what the situation was 99% of the time. Little more was said beside "you're good," "not yours," or "go my way" which like all aspects of the trading pit was centered on brevity.
Each exchange had it's own idiosyncrasies in comparison to my experience at the CME, for example the traders/brokers at NYMEX fling their cards into the center pit reporter for the exchange to enter and "outtrades" are referred to as "cutouts" at KCBT, etc....