'Late Veneer' on other planets
This is an important and pertinent question to help understand the 'late veneer' process on Earth.  To do so, understanding how it may have occurred, if at all, on the other terrestrial planets (Mercury, Venus, Mars and possibly the Moon, even possibly the rocky moons of other planets).  If there is no evidence, then that sheds light on another aspect of the uniqueness of Earth.

For practical reasons, my answer will focus on Mars and Venus, as according to an article specific on the topic, Dynamical and collisional constraints on a stochastic
late veneer on the terrestrial planets (Raymond et al. 2013), that asserts that the late veneer was


  an accretionary phase for Venus, Earth and Mars but an
  erosive phase for Mercury and the Moon.


There are obvious difficulties in fully answering this question; however, Raymond et al. assert that evidence exists of 'late veneer' like activity for not only the Earth, but for the Moon and Mars, from the article:


  Evidence for the late veneer comes from the existence of highly-siderophile
  elements (HSEs) in the mantles of Earth, Mars and the Moon. Simply put,
  HSEs are “iron-loving” elements that tend to partition into metal and should
  thus be removed from a planet’s mantle during core formation. 


Mantle samples are taken from Martian meteorites that have landed on the Earth and are detailed in the paper Evolution of the martian mantle inferred from the $^{187}Re$–$^{187}Os$ isotope and highly siderophile element abundance systematics of shergottite meteorites (Brandon et al. 2012) who observe the observations made by Raymond et al. as


  The
  measured concentration of HSEs in the Martian mantle is similar to the
  Earth’s (Walker, 2009; Brandon et al., 2012).


Based on a conclusion made by Brandon et al. that


  The relatively high HSE abundances in both planetary mantles likely cannot be accounted for by high pressure–temperature metal–silicate partitioning at the bases of magma oceans, as has been suggested for Earth. If the HSE were instead supplied by late accretion, this event must have occurred prior to the crystallization of the last martian magma ocean.


According to Raymond et al. the situation for for Venus and Mercury, the late veneer is modeled to have possibly affected their retrograde motion, but the authors admit that this is is speculative.

In the absence of sufficient samples from Mercury and Venus, it is modeling rather than sampling that the authors use to hypothesise the possible effect of the Late Veneer on them.  Given Venus' size, it is likely that it, alongside Earth were the 'primary targets' of the late veneer bombardment.


  Additional references:
  
  Walker, R. J. 2009. Highly siderophile elements in the Earth, Moon and
  Mars: Update and implications for planetary accretion and
  differentiation. Chemie der Erde / Geochemistry 69, 101–125.
  
  Walker, R. J., M. F. Horan, C. K. Shearer, and J. J. Papike 2004. Low
  abundances of highly siderophile elements in the lunar mantle:
  evidence for prolonged late accretion. Earth and Planetary Science
  Letters 224, 399–413.