This isn't even accounting. It's just bookkeeping.
Real money-handling systems have
"reconcilation", where, usually daily, there's a break and the day's journal of transactions and all account balances are captured. Then they're checked against each other and external sources (i.e. does your internal calculation of what's in bank accounts and storage match the bank's numbers). They won't always match, because of outstanding transactions, all of which must be accounted for. Discrepancies that can't be accounted for indicate trouble.
Most real businesses that handle money do this every day. If they've been ripped off, they know quickly, which narrows down the number of suspects and limits losses. Mt. Gox
never did it.
This stuff isn't rocket science. Your local supermarket manager is very familiar with this process. A big supermarket has many checkout counters, many clerks, cash all over the place, credit card transactions of several kinds, merchandise going in and out, and a very small markup. Probably a higher transaction rate than Mt. Gox. Yet if money goes missing in a supermarket, it will be noticed within hours, and who took it will probably be known, and shown to cops if necessary, the same day.
There's a reason that most Bitcoin exchanges fail, and it's cluelessness, not technology.