Introduce some damping
From an engineer's perspective, this looks a lot like an undamped system, in which a multitude of small inputs can amplify resonances, resulting in large swings which can ultimately destroy the device. (Have you checked your car's shock absorbers lately? :-) From what I read above, comparing bids and asks every second sounds perfectly reasonable.
Any attempt at millisecond trades would be pointless. If one person entered a multitude of bids and asks at sub-second intervals, the result would be worked out only on the tick, matching offers in first-come, first-served order. Sales (and price changes) would occur only once a second, preventing the out-of-control swings requiring shutting down a market. Of course, you'd have to introduce some jitter in the timing (say, make the tick a value between 0.8s to 1.2s, varying randomly) to prevent people from trying to game the tick. And each instrument would have its own clock---you don't want to update every issue on the market at the same instant.
As is probably evident, I'm no trader. If there's a better way to add damping, go for it, but the cost of missed opportunity at the millisecond would be more than repaid by avoiding the cost of a market crash. (At least to society at large. I feel no pain at the traders' making a fraction less than the current system offers.)
I can hear the screams now: ``But..., but..., you're introducing, *gasp*, _inefficiency_ into the market!'' No fecal material, Sherlock. Your shock absorbers dissipate some of the engine's power, introducing inefficiency, too. But where's the efficiency in hitting a tree because your wheels were bouncing wildly?