Decrease of magnetic Field: Earth shielding against deadly particles and deadly radiation coming from space, has a name: Magnetic field. The planet rotation generates a non-inertial force called "Coriolis force". The likely most accepted theory for generation of magnetic field in celestial bodies is called Dinamo Theory. Convection moves electric conducting fluid in the mantle and outer core, inside our planet. By symmetry, it is easy to note these are radially symmetric, with no preferential direction. This creates minimum magnetic field outside. However... Earth spins. This spins generates a non-inertial force called coriolis force, which organizes the convection currents into columns, generating a magnetic field aligned with the rotation axis. If earth rotation decreases, so as Coriolis force, and so as the strength of Earth's magnetic field. And then, high energy charged particles or plasma coming from the sun or interstellar winds, would reach the planet easily.
Escape of atmosphere: The constant solar wind (which is now is no more being diverted by the magnetic field) would hit molecules in Earth's atmosphere head on, transferring momentum to them. This means, more and more gas molecules of atmosphere reaches escape velocity and leaves the planet. The atmosphere would then become more and more thin until it fully vanishes. That's precisily why some large moons and even planets have no or very little atmosphere: Because they have no magnetic field. With less and less atmosphere, there will probably some unbalance in the known natural cycles of some gases (say.. nitrogen, oxygen, etc).
Radiation: We have two shields against deadly radiation from space: Magnetic Field and atmosphere. Solar and interstellar winds and radiation could react with the Earth's elements in the atmosphere, destroying it by making them react to produce something else, decreasing our shield strength against cosmic radiation. For example: Alpha + beta radiation can produce ozone from an oxygen molecule. People exposed to such level of radiation because atmosphere is not protecting as it should, perhaps could lead to ARS. Also, high energy charged particles (electrons, protons, positrons, ...) from solar wind, for instance, when meets a neutral atom can produce high energy photons (including gamma rays). If there is no magnetic protection to prevent this meeting in the first place, gamma radiation produced in Earth's atmosphere would increase.
Beryllium-10: Radiation (now in higher levels) might increase concentration of Beryllium-10 in Earth's atmosphere, which is an radioactive isotope and decays into beta radiation. Not sure about the consequences of this, but its probably safe to say there would be a rise in the incurable lung desease known as Berylliosis. For more information take a look here and here.
The movement of heat: A nice example to look the power of heat movement, is the Southern Ocean, at 60 degree south. The sea there is restless. The reason is the movement of heat, from the equator to poles causing: oceanic currents, persistent winds, storms, which moves over 130 million tons of water per second. Heat transfer is very powerful. Now... rotation decreased..The same that happens between equator to pole, might happen between the day and night sides. Heat will move seeking a thermalization of both sides. We are talking about storms, or worse, with unprecedental proportions, frequences and sizes. Also, we may even get powerful convective persistant winds in lower and upper atmosphere, between night and day sides.
Storms: In very simple terms... the sky is clear and sun is delivering its energy to ocean (240hrs of energy!). The water heats up. When some critical temperatures is achived, vaporization levels starts to rise significantly, causing vertical winds. Water vapor at certain altitude, releases heat and condenses to cloud, raising temperature of surrounding air, making clouds in turn rise further, producing more vertical winds. It will grow and grow and continue until the clouds block sunlight. Earth rotation forces the air to rotate forming hurricantes. However, there is no earth rotation in this case.. And as said later, there is convective persistant wind (probably, very powerful ones). This storm would be carried out by convection from the day side to the night side. Movement of this masses causes friction and thus build up of static electricity. We are talking about heavily charged clouds with tons of water inside, moving to transfer heat from day to night side. And since 240hrs the day.. its much water in this clouds....! Imagine the size... With normal Earth rotation, such events already can be seen from space.. Imagine this one.
EDIT: About the comments of the origin of the magnetic field of Earth.
This is actually a magnetohydrodynamical system explained by Dynamo Theory. The magnetic field is indeed also caused by convection. However, convection does happen because a temperature gradient between the inner core and Earth's surface. This means the fluid movement would be symetrically radial because the temperature gradient is approximately radially symmetric. And this implies no magnetic dipoles. The Coriolis force makes those convections currents be organized in columns, and then it induces the appearance of a magnetic dipole (with North pole and south pole). This means, the convection and the Coriolis force together, creates the field. There would be no magnetic dipole if there were no convection, or if there were no Coriolis force.
Without the coriolis force, the magnetic field can be approximated to the field of torus coil. And this is known to be strong only inside the coil, and not outside. Which means, the magnetic field lines would concentrate likely almost completely inside the planet.
EDIT: About the comments of Ganymede moon
Ganymede is indeed tidally locked, and indeed has a magnetic field. But this situation is beyond the scope of my answer (which dealt only with Coriolis and convection). According to this paper however, they say they can't be sure about the cause of the field, but one model is a "permanent magnetic dipole field [...] superimposed an induced magnetic dipole driven by the time varying component of the externally imposed magnetic field of Jupiter’s magnetosphere", quoting their worlds. Which means, it is really the presence of the strong external field of Jupiter which causes this particular moon to have a magnetic dipole. They of course has other models, however, the model of the moon itself generating the magnetic field is done at the order of magnetic quadrupole moment, suggesting more complications about the cause.