At a point when the audience is still unsure of who these characters are, the last thing that should have been done was an episode where their worst vices are magnified.
You mean like in "The Naked Time"? Or "The Naked Now"?
When you put characters under pressure, you learn things about them that you would otherwise never know. That's the fun of episodes like these. I can see why the writers would do it right off the bat -- to help the viewers learn more about the crew.
Honestly, I think those episodes suffer horribly by placement myself - sure, it's a chance to see the characters reacting differently... but so close to the start, the audience is still learning about how the characters react NORMALLY. An episode where the characters do things they wouldn't normally do is served best by already knowing the characters. If you have to have it in the first season, have it late in the first season. Preferably, have it in the second season. Episodes like this are worthless when you don't have context for the characters - seeing a character let loose after two or three episodes isn't the same as seeing them do so half a season down the line, when they've been bottling things up for so long.
'Right off the bat,' in my opinion, is the wrong time to play the 'characters do strange and out-of-character things under influence.'