Bad things. Lots of bad things.
First off, there is a term for the version of "not rotating" that you're after. You're looking for it to stop rotating in the sidereal frame. The sidereal frame is what you would see if you looked at the earth from one of the constellations. The Earth is not rotating about its axis from this perspective, but you will see a year-long day/night cycle.
You are right about how the Coriolis effect will basically be out of play. Your angular rate drops from $7.272 × 10^{-5} \text{rad/s}$ (Earth's current rotation rate) to $2.042 × 10^{-7} \text{rad/s}$. The Coriolis term is directly proportional to this, so expect to see a roughly 300x decrease in the effects of the Coriolis effect. All of our nice predictable weather patterns which rely on Coriolis to create easy to work with atmospheric cells go out of the door. Fortunately, we're going to make new ones.
Our temperature balances all center around the day/night cycle. You would basically be removing that from play. Life is about to get really miserable. You're going to have a hot spot on the Earth, wherever it is day. This is going to create a large mass of hot air rising very quickly off of the plains. This air will be displaced by air from the twilight regions of the planet. Large, very angry convection cells will form.
How angry? Well, consider the part of the planet most directly in line with the sun. The only air cooling it gets is going to be from the hot air rushing in nearby. All of the cold air from the twilight regions is going to be heated up as it travels over the rocks (it stays low because it's cold air). This heats the air up, causing it to lift away. You won't get one big convection cell the size of a planet. You'd get dozens, each one hotter than the next.
And in the middle? Well, let's just have a reminder of how hot the Sun is. Build a solar oven. You use mirrors to increase the power of the sun by maybe 4x, and then you isolate the hot box from the outside world. The isolation is actually the important part. If you could get nice insulating glass, you could cook food without needing mirrors at all. Solar radiation is $1.4\text{kW}/\text{m}^2$. Each square meter of land is getting more solar energy than a commercial grade microwave on "high". There's a reason you can cook your food this way!
The temperature gradients probably wont let you get to "glowing," because at that point the equations get more interesting (you start radiating energy out into the cold of space, which keeps you cool). However, temperatures will easily reach oven temperatures, without any trouble.
On the other side of the planet, you have several months where you cannot see the sun. At this point, radiation of thermal energy will come into play. The sky is roughly $-40^\circ\text{F}$ You're going to be dumping a lot of energy into the sky. Consider a desert where we have clear skies (clouds make the sky "appear" warmer). It is not unheard of to have a nice 60°F day (15.5°C), but when the sun goes down, the radiation effects emit so much heat into the cold sky that you can wake up to find ice on the ground. This happens over the course of a few hours. Imagine what 6 months of that would do.
Unlike the hot side of the planet, we don't get convection cells here. The cold ground chills the air, rather than warming, creating a layer of cold air near the ground. With such a smooth temperature section of the globe, there won't be much wind to disrupt the wind. The only effects we will see are radiative. And, since there's no wind, there's nothing to push moist air into colder regions to make clouds. It would just be a cold cold cold desert sky for months on end. At some point, you would start to chill the atmosphere enough to see a sky that appears to be even colder than $-40^\circ\text{F}$.
So what does this mean for geology?
Even the rocks are going to have a hard time. One of the most powerful erosive forces in the world is ice. Water seeps into cracks and then later freezes. The expansion of ice breaks off huge hunks of rock. Temperature gradients like this one are going to give ice a run for its money. A yearly expansion-compression cycle of 500+ degrees is going to cause anything resembling a hard rock to crack into dust. The surface would be littered with only soft materials that can flex. Mica might be a good example, as would clay.
However, the soft materials won't have a good time either. Consider the windy seasons. Yes, seasons. Twice a year, your particular spot on the globe is going to be in the twilight, on the edge of the strongest convection cell on the planet. Massive winds are going to pound you from above. On the leading edge of the hot zone, you'll get torrential downpours because the heat will evaporate the water that deposited when it got cold. It will be flung high into the air to turn into massive rainclouds the likes of which the world has never seen. This wind and rain would pummel any soft materials into dirt. Since the world has lots of dirt, the edges of these convection cells will create massive multi-kilometer high dust storms.
What about the poles? They fare better. The closer you get to the poles, the more time you spend in twilight. However, most of the nasty wind/rain effects are going to be found along east-west lines. You'll get less of it in the north and south. Unfortunately, there's a problem here too. These are still the poles of the Earth. They still only get glancing sunlight, so they are just as cold as the Arctic or Antarctic is today!
I want humans to survive in this!
You are a sick individual for subjecting your citizens to this world. Your best bet is to invent space travel and get off this rock before Superman stops its rotation!
No luck? Well drat. Okay, it's survival time.
There is no way to survive at equatorial latitudes. There simply isn't. Unless you are an amazing ocean-faring race, there's no way to just keep outrunning the hot zone. Once it hits you, it's over. Digging holes might work, but the fracturing rock makes it likely you wont be able to dig yourself out before the cold hits.
Just like nowadays, surviving at the poles is not an option.
The solution is to live on a belt just below the arctic. The Inuit might not even notice that the earth stopped spinning. They live with months of no sun already. They would, however, notice that the winds are getting trickier to deal with.
A little further down, you might be able to have a band of nomads which continuously circle around the world along the twilight. These are the regions that are getting subjected to extreme conditions, so you wouldn't get to stop moving. You would have to stay with the twilight. Land bridges would be key.
What survives on this planet? Well, along that magic band, plants may be able to wait out the winter and quickly thrive in the windy seasons. There would be abundant food if you found these. Plants would have to spend so much energy reproducing each year that they wouldn't be able to stop you from eating a little without seriously jeopardizing their survival. Arctic water creatures would fare well. If you had a sufficiently flat world, there might even be a river system which equatorial creatures could use to traverse across continents (I'm thinking of the most epic whale migration imaginable).
In all, it's a bitter world to live in.