Only the combination $CPT$ of the charge conjugation $C$, of the parity reversal $P$ and of the time reversal $T$ is expected to be fundamentally true and is true in any local Lorentz invariant quantum field theory (in the Euclidean theory $CPT$ becomes a rotation of angle $\pi$, which is continously connected to the identity in the rotation group and so is obviously a symmetry). In fact in the Standard Model $CP$ and so $T$ are violated. This was first experimentally observed in 1964 in the study of kaons, see http://en.wikipedia.org/wiki/CP_violation and is explained by the existence of three generations which allow for a non-trivial $CP$ violating phase in the $CKM$ matrix. Another possible source of $CP$ and so $T$ violation in the Standard Model comes from the theta angle of $QCD$ but experimental bounds show that the theta angle is very near to zero.

Obviously these microscopic violations of $T$ have nothing to do with the macroscopic thermodynamical arrow of time. Most of the macroscopic phenomena are controlled by $QED$ which is $T$ invariant.

A non-trivial electric dipole moment for the electron or the neutron would be a sign of $T$ and so $CP$ violation. Indeed by general principle the electric dipole moment $\vec{m_e}$ is expected to be proportional to the spin $\vec{S}$: $\vec{m_e}=\alpha \vec{S}$ for some $\alpha$. But under $T$, $\vec{S} \mapsto - \vec{S}$ and $\vec{m_e} \mapsto \vec{m_e}$ (to remember these transformations it is enough to look at some naive classical expressions) and the electron remains an electron and so if $T$ is a symmetry, $\alpha=-\alpha$ i.e. $\alpha=0$. Similarly one can show that a non-trivial electric dipole moment violates $P$ but preserves $C$. Remark that most electrically charged particles have a non-trivial magnetic dipole moment, proportional to the spin. This does not violate $T$ or $P$ because a magnetic dipole moment transforms under $P$ or $T$ in the opposite way of a electric dipole moment.The observed $CP$ violation in the Standard Model implies the existence of a non-trivial electric dipole moment for the electron but it is a very indirect effect and the expected contribution is so small that it is out of reach experimentally.

I think that a magnetic monopole does not violate $T$ or $CP$. Indeed by $S$ duality we expect a monopole to have a electric dipole moment and to preserve $T$ as an ordinary electron with an magnetic dipole moment preserves $T$. Similarly a magnetic monopole with a non-trivial magnetic dipole moment will violate $T$. A possible confusing point is that the $S$-duality does not commute with $P$ and $T$. Indeed $S$-duality is essentially applying the Hodge star to the 2-form field strength and the Hodge star depends on a choice of orientation which is reversed by $P$ and $T$.

A dyon, i.e a particle with both electric and magnetic charges, violates $CP$, and so $T$ if its electric charge is not appropriately quantized. In a theory with pure electric charges, it is known since Dirac that the magnetic charge is quantized but one has to use $CP$ symmetry to also prove the quantization of electric charges of dyons. The fact that a non-trivial theta angle implies non-trivial electric charges for dyons is called the Witten effect.