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The original three-song release from 1984 was the most brutal thing ever put out, at that point in time. Hell Awaits and Reign in Blood would further stretch the envelope, but it was this EP, and one song specifically, that completely demonstrated the raw violence that thrash metal was capable of.
That song is none other than "Chemical Warfare". This was the logical successor to "Black Magic", which had appeared in the Slayer live setlist in 1983, but was really not all that intense, compared to other stuff that was available by the time Show No Mercy came out in 1984 (the album was delayed for about three months due to record label vagueries, a similar fate would befall Exodus, whose Bonded by Blood album should have totally destroyed all in its path in the summer of '84, but didn't actually arrive until 1985, but that is a completely different story.)
"Chemical Warfare". Lots of riffs. Insane lyrics. Total fucking brutality. The song that inspired everyone from Paul Baloff to Gene Hoglan to be faster, harder, and even more uncompromising than before. Yeah, and lots of quality riffs. There's a section that is Judas Priest's "Steeler", on crack, and about 48 other excellent riffs. There is nothing from '84 that's heavier than this, except maybe "Feel the Fire" from Overkill's second demo or the Possessed debut demo - but as far as actual studio releases go - no competition.
The other two songs, "Captor of Sin" and "Haunting the Chapel" are also very good in their own way - a bit closer to the Show No Mercy sound, though still quite brutal in the guitar tone and riffage. Haunting the Chapel has a similar intro riff to Aggressive Perfector but then goes completely heavy on us, while Captor of Hell is most similar to Die By the Sword with the vicious thrash break, times a million. "Hot... winds of Hell... burn in my way!!!" These two would, given the same production as Show No Mercy, not stick out.
The re-release of this EP includes "Aggressive Perfector", the 1983 version that appeared on Metal Massacre III. A speed metal song that would not have been out of place on Show No Mercy.
I think that there is in fact a version of Show No Mercy out there that has these 4 songs as bonus tracks. You figure out which song sticks out the most. :-)