I'm not sure how much I can comment about it, but here we go (that's a joke... maybe).
Is it realistic in the collapse of the current system? Well kind of, but not in the timespan that is suggested. But that was a big part of the movie. It has also been mentioned to me that in one of the points of the movie, they actually show the thermohaline circulation going in reverse, but that is the least of my concern (and I am not about to rewatch the entire movie for the 5 second clip that I couldn't show you).
Is it realistic in the effects of that movie? No, absolutely not. No, synoptic scale low pressure systems are restricted in size to the length scale of the Rossby Radius of Deformation. Moreover, the sinking of air would actually increase the temperature of the air, similar to Chinook winds (called adiabatic warming). A "back of the envelope" estimation of this is that air brought from the tropopause to the surface could be approximately 188°F (87°C), as the dry adiabatic lapse rate is 10°C/km, the height being 10 km in the midlatitudes at a temperature of about 260 K. Then, there is the issue of sinking air being associated with high pressure (clear skies, as the warming air evaporates water and is usually dry as there is less water further from the surface), and not low pressure.
So is it accurate? In terms of the circulation, they only fast forwarded a couple hundred to thousand years. But even that statement is inaccurate to some extent, as it is projected to weaken, rather than collapse outright. In terms of the meteorology/climatology, absolutely not. Still, it's enjoyable nonsense.