Star Trek, season 1, episode 4: The Naked Time. In the very first segment, a red-shirt takes off a protective glove, puts his hand on a surface while working on something, unwittingly gets a mysterious substance on his hand, scratches his nose with that hand under his protective hood, and then puts his glove back on... Quarantine time!
Is there an episode where a red shirt doesn't do something questionable that doesn't end in death (besides Scottie, of course)?