I'd make sure I played it as a noticeable feature of the character.
In our 1e game my Paladin only had a Dex of 6.
Mechanically all this did was cause a 1pt AC penalty. And of course make it a lot harder for me to pass dex checks (you wanted to roll = or less). I can easily deal with these effects. Get better armor/more magic +s, avoid doing things where dex is a major factor (climbing around in the rigging of a ship for ex), or taking extra precautions (if able) when I must take a risk.
RP wise? At least once a session I'd occasionally roll a random dex check against myself - when operating in poorly lit conditions, on stairs, fighting on the wet decks of a ship, etc. And since we spent ALOT of time in the Underdark....