I won't address the almost doubled obliquity (axial tilt) since you didn't ask that specifically, but it will have huge effects and probably deserves its own question. If the radius is going to change by more than 500-1000km or so, that probably deserves its own question as well. In thinking about quadrupling the angular velocity of an Earthlike planet, there are a few areas I can think of right away:
The planet will be more oblate (squished at the poles and fatter at the equator). I don't think it's worth the calculation since the effect is so slight, but this will lead to a slightly higher gravity at the poles and lower at the equator. However, there is a larger effect that is not really gravitational but belongs in this section. For a rotating planet, there is a centrifugal "force" acting outward which is strongest at the equator and nonexistent at the poles. This will make the perceived gravitational force at the equator ~5% less than at the poles, with the difference decreasing as one moves toward the poles. This would be barely noticeable for a person day-to-day, if at all, but this would have major effects on the world ocean. The sea level near the poles would drop, and near the equator it would increase. I don't think I know how to make this calculation right now, nor do I have the time to learn, but I would love to hear from someone who has a guess about what the effect would be at the equator in terms of sea level. I guess I am also thinking about this as if it suddenly happened on Earth, but if it were a planet that had always been that way it probably wouldn't be a huge deal.
The altitude of a geostationary orbit would decrease by over half, from ~42,000km to ~17,000km (EDIT: the numbers I gave are orbital radius - the altitude would decrease from ~36,000km to ~11,000km). This would have lots of implications for how these satellites would operate (close means easier imaging but also narrower field of view). Also, rockets are normally launched (at least partially) eastward and nearer to the equator to take advantage of the Earth's rotation. With increased angular velocity this would still be the case but it would be much easier to get into space, whether for low orbit, geostationary orbit, or interplanetary travel.
The Coriolis force acts at a right angle to the motion of an object not attached to the surface (rightward in northern hemisphere, leftward in southern hemisphere). This doesn't have many implications for day-to-day life, but if you are e.g. a pilot or an on an artillery crew it is pretty important. The Coriolis force has a magnitude of the multiplication of the object's velocity and the angular velocity of the planet, so quadrupling the angular velocity would quadruple the Coriolis force.
More important than ballistic trajectories and powered flight, the Coriolis force has a major impact on climate. At the large scale in the oceans and atmosphere, the dominant currents are geostrophic. This means there is a balance between pressure gradients and the Coriolis force, so winds/currents move parallel to pressure gradients. Not to be too complex here, but the point is the Coriolis force is a huge part of how the atmosphere and oceans circulate, and I can't say exactly how this would change. I can say that geostrophy would still dominate, and large storms like hurricanes would spin faster.
The total insolation would stay the same, but with a much faster day/night cycle. So while the climate may not actually change drastically with this one, there might be some large local effects. I can think of things like shoreline winds and precipitation in dry areas.
Does your planet have a moon/moons? Does it specifically have an abnormally large (compared to its size) moon like Earth does? If so, the tides will change pretty drastically. The periods of the tides on Earth are all combinations of aspects of the Earth's rotation and the orbits of the sun and moon. So the periods of tides on your planet will be quite different. The magnitude of tidal variations is very dependent on bathymetry, but I can say any tidal bore would be more intense than it otherwise would be.
Currently the moon also "steals" some angular momentum from the Earth via tidal friction, and if the angular velocity were quadrupled this effect would increase. This would still be negligible in the course of day-to-day life or at the scale of human lifetimes.