When the coaxial cable is in the near field of a center fed, 1/2 wavelength dipole and it does not run perpendicular to the antenna, it is subjected to imbalanced near field currents. The coupling effect will be cos $\theta$. The result is that the exterior braid of the coax may carry common mode current. OCF and end fed antennas also promote common mode current due to their inherent imbalance. Running the coax parallel to the dipole should be avoided.
The significance of the common mode current is dependent upon factors such as coax length, the grounding of the coax, common mode chokes, the frequency of operation, imbalance of the antenna, etc. Antenna modeling programs can be used to estimate the subseptibility of a particular configuration.
The effects of common mode currents can include RF shocks in the shack, interference with home electronics, coupling of nearby RFI into the antenna, alteration of antenna resonance/SWR and an alteration of the antenna pattern and gain.
A common mode choke at the feed point of the dipole and another one at the shack entrance or at least out of the near field of the antenna can be deployed to mitigate the effects. Ferrite based common mode chokes or 1:1 current baluns tend to be the best multiband performers. Some report success by burying the coax.
It is also helpful to avoid odd multiples of 1/4 wavelength coax as this promotes the formation of common mode currents. Note that the coax velocity factor does not come into play since this current is on the exterior of the braid. Instead, use a 0.95 to 0.97 velocity factor to account for the outer coaxial jacket.