First, I'll adopt terminology from Ringworld: "spinward" is in the direction of spin, and "antispinward" is opposite the direction of spin. And I'll say a bit about the Coriolis equation, but then go into qualitative effects.
Basically, anything that involves "up", "down", spinward or antispinward motion (which captures the fraternity-party activities in the comments), and a few other things, will be different from a "normal" gravity environment. The Coriolis equation $$\mathbf a_c=(-2 \mathbf \Omega \times \mathbf v) - \mathbf \Omega \times (\mathbf \Omega \times \mathbf r)$$ is opaque to most people who aren't scientists, engineers, or mathematicians, but it tells us what's going on.
The second term, $$- \mathbf \Omega \times (\mathbf \Omega \times \mathbf r)$$ is just the "artificial gravity" you feel. For a fixed rotation rate ($\omega$, the magnitude of the rotation vector $\mathbf \Omega$, so your "RPM") it varies only with your distance from the rotation axis, as long as $\omega$ takes into account any motion spinward or antispinward with respect to the station or spacecraft. The farther from the axis, the stronger the artificial acceleration, in direct proportion.
It's the first term, $$-2 \mathbf \Omega \times \mathbf v$$ that causes most of the trouble with our Earthly intuition about motion in our surroundings. It involves a vector cross product of the vectors $\mathbf \Omega$ and $\mathbf v$. $\mathbf \Omega$ is just the rotation rate $\mathbf \omega$ coupled to the direction the rotation axis points, and $\mathbf v$ is just the velocity vector as measured in the rotating reference frame. That cross product causes accelerations in a direction perpendicular to the velocity (and also perpendicular to the rotation axis), most un-intuitive if you've just come up from Earth for the first time.
OK, some observable effects.
You've already mentioned a couple: running spinward makes you feel heavier, running antispinward makes you feel lighter. If you could run antispinward at the same speed that your surroundings (hopefully, a tunnel!) are rotating, the first Coriolis term would exactly balance the second, and you'd be weightless. You could just float in the tunnel as the station spins around you—until a bulkhead comes up, then Whap! But it's tough to run that fast, for two reasons: the faster you run antispinward the less "weight" (artificial, of course) you have, so the less traction you have; and in stations or spacecraft of any decent, motion-sickness-preventing size, that speed is high. For a 100 m radius station, getting a measly lunar g (1.625 $\frac{m}{s^2}$) requires a rotation speed at the 100 m radius of 45.9 km/hr (28.5 MPH). Good luck getting up to that speed. And if you do—good luck with that bulkhead!
Motion away from the rotation axis ("downward") appears to induce antispinward forces, and "upward" motion sends things spinward.
An example: you're starting to take a shower. You know when the flow starts it will be very cold, so you don't stand directly beneath the showerhead, which is oriented to send water straight down. You turn on the flow slowly thinking you'd avoid sudden surprises. But you chose to stand antispinward of the showerhead, and to your great discomfort, the flow of frigid water that emerges from the showerhead straight downward curves antispinward, right onto you!
If, when you reacted, you jumped straight upward, you wouldn't land on the spot where you left, you'd land spinward of that spot. Out of the water flow, hopefully.
Motion parallel to the rotation axis doesn't get any such wierdness, until the downward acceleration of the artificial gravity induces an outward velocity, then the antispinward curve begins.
In my discussions with various folks contemplating the design of large rotating stations, the idea of sports on such stations has come up. Traditional sports such as basketball would be exercises in frustration as balls, shuttlecocks, etc., and you, move in ways you're simply not accustomed to.
