1) very modest Coriolis force
2) centre of heating and uplift is equatorial

(1) - although the planet is tidally locked, it is actually still rotating, ONCE every orbit. (Day = Year). for a close-in orbit to a small red dwarf, a "day" of several tens of Earth days is likely. Venus still shows some atmospheric vorticity with its 243 earth-day rotation, so modest vorticity is likely in this scenario.

(2) there will not be "A hurricane" at the equator, but likely a pair of hurricanes in the tropics - one north and one south of the equator, lagging the planets rotation to occur about 20 degrees away from the sun-facing point. For more complex atmospheric patterns, multiple sets of hurricanes will exist, either stably, or in migrating wave-like patterns. The option to interact with the fixed ground surface may allow these circulation patterns to become "burned-in" to topography or albedo features, or perhaps these will migrate with time - giant dune belts at the core of slowly-migrating hurricanes?

And, of course, on the darkside you have the options for icecaps and glaciers, and a twilight sea or rivers and lakes at the snouts of melting glaciers.

These tide-locked planets with atmospheres are quite interesting to speculate about. We have nothing exactly like this in our solar system. (a cooler Venus is the closest thing we have, or the winter polecap of Mars)

Oh, and DO read the original paper, because the first thing they point out is that Gliese 581 d is colder than mars, and G581 c is hotter than Venus. The rest of the paper is spent trying to salvage something from this. If you tidally-lock G581d you make it worse. G581 c *might* be salvageable, but it really is too hot. You have to invoke an atmosphere thinner and less efficient at heat transport than our Venus. (And if you're forcing the atmosphere to thin, when does this process stop?)

There's room for much more work in this area. I look forward to the next decade of research on atmospheric dynamics in these situations...