Trailing Stop Order - how often do they get executed due to an error?

I've never experienced it with any of the brokers I've used. The "miscalculated ticks" are rare - certainly not frequent enough to keep you from using trailing stops.

Make sure to use a limit on the trailing stop. In that case, even if you did get stopped out accidentally, you could always rebuy at a similar price

It almost never happens because if it did too often, they would lose customers. The only thing that you need to worry about is the first case of system outage where they go down and can't operate normally. It is to their benefit to execute your order to the best of their ability (Most of these companies will also have things in their terms which state that they keep the customers interests at the forefront so you could take them to court if they screwed you over... then again that is expensive as hell)