Should we be looking for extra-terrestrial life on comets?
Yes we should be and we are! Scientists have been analysing cometary material - but its a challenging task. The problem with looking at meteoritic material from comets on Earth is that it is generally contaminated with material from Earth. In addition, meteorites get physically altered during their passage through the Earth's atmosphere due to the high temperatures of re-entry.

So, the trick is to send missions to the comet. However, then the difficulty is in designing a mission that can analyse samples in situ. NASA's Stardust mission got around this by sample return to Earth. The probe visited comet Wild-2 and found the amino acid glycine among other interesting organic compounds. However, no evidence of life was found (metabolic products, organisms etc.) Further missions to comets (and asteroids) are planned, but they are not going to explicitly look for life. 

Elsila, J.E., Glavin, D.P., &amp; Dworkin, J.P. 2009, Meteoritics and Planetary Science, 44, 1323