From your description of the rotating cylinder's habitat, it sounds like we can consider it to be in basic isolation. There are stars and such in the sky that appear to move in regular intervals across the sky, but they all just track half circle motions. This would be akin to watching the stars move in the sky at the Earth's equator.
The way to distinguish a non-intertial reference frame from an inertial reference frame would be to measure "spooky" unidentified forces that appear. In the case of a rotating reference frame, these would correspond to the Coriolis force and the Centrifugal force. In an inertial frame, the force on an object is
$F = m\vec{a} = m \frac{d^2\vec{r}}{dt^2}$
however in a rotating reference frame, this becomes
$F = m\frac{d^2\vec{r}}{dt^2} + [2m\vec{\omega} \times \frac{d\vec{r}}{dt}] + [m\vec{\omega} \times (\vec{\omega} \times \vec{r})]$
Where $m$ is the mass of an object, $\omega$ is the angular velocity vector of the rotating reference frame, i.e. how fast the cylinder is rotating and in which direction, and $\vec{r}$ is the position of the object in the rotating frame (note: I use $r$ to emphasize that, since this is a cylinder, the easiest coordinate system to use, for our purposes is the cylindrical coordinate system). Where there are two new terms (note: the $\times$ symbol above is a cross product, which is very important since we are dealing with position, velocity, angular velocity vectors). The first is the Coriolis force and the second is the Centrifugal force.
Deviations from Earth
It is very important to realize this is a different case from Earth. Many of the "spooky" effects of the rotating frame are easy to notice on Earth because one can change their distance from the rotation axis, e.g. by traveling from the Equator to the North Pole, and the direction of the force changes with respect to our horizon (ground).
Ex: Centrifugal Force always points outwards from the rotation axis. At the equator it points perpendicular to the ground (straight up in the sky). At higher latitudes, it will not be perpendicular. In our case, the centrifugal force will always be perpendicular to the ground.
Centrifugal Force
Probably the first to come to mind, if we look at the third term it depends on the objects position and how fast and which direction the cylinder is rotating. It will change the perceived force of gravity of an object by some amount and could theoretically be measured, given a knowledge of Newton's Law of Gravity $F=mg$, however it is most readily noticed by its varying effect due to changing an objects position. Unfortunately for your scenario, due to the cylindrical symmetry all points on your cylinder experience the same Centrifugal Force, and hence it is more likely that its effect would be folded into the gravitational force, i.e. $F=m(g + C)=mg'$ for some constant C
Coriolis Effect
This one depends on the rotation and the velocity of an object. You may be familiar with this causes objects to change from straight line trajectories when traveling West/East on Earth, but this does not occur at the Equator. What happens instead is that objects will deflect upwards or downwards, depending on if they are traveling the same direction or opposite direction to the rotation of the cylinder (see Eotvos effect).
What this means is the only deviation you could observe would be that the force of gravity would increase/decrease depending on which direction you were traveling in, by a magnitude:
$\Delta F = 2m\vec{\omega} \times \frac{d\vec{r}}{dt}$
The greatest deviations would be seen between an Westward and Eastward moving object. But how could you possibly measure this?
Measuring the Coriolis Effect
The magnitude is determined by how fast your cylinder is rotating and how fast your object is traveling. You can tune this to your liking for plausibility reasons.
Measure with a gravimeter. Basically a spring with a weight on it, where you measure the compression of the spring to determine the gravitational force. Put it on something traveling west and something traveling east. This depends on the technologically prowess of your civilization, and likely your best bet for traveling object would be a boat. Things like waves would probably ruin any sensitivity your gravimeter had and the boat would be too slow moving.
Measure changes in how fast things fall. I could envision an experiment where you fire a cannonball (or similar projectile) towards the East and measure the time it takes to fall (or distance it travels) and then repeating by firing the cannonball to the West. There will be difference in fall time/distance traveled, but the scale of this might be too small given other sources of error (such as elevation changes, precision of measurement).
Both of these greatly depend on what technology is available and how scientifically advanced your society is. Remember there are limitations to how fast you can spin your poor natives before they fly off or something. And more importantly there should be a reason to try some of these experiments. No one spends lots of time and effort on an experiment unless they expect to see interesting results, especially if they risk their reputation, or worse, their life.
