Recently, my bike often develops a front wheel wobble when I ride hands-free at slow to moderate speeds. The wobble quickly deteriorates, to where I think I'd go down if I didn't return my hands to the bar. It doesn't always happen - but often enough.
Wondering if the cause for the wobble was an issue with the front wheel, I checked for trueness. I've had my bike and its wheels for a little over a year and have put about 5000 miles on it, so some imperfection might be expected - but I'm not sure how to judge the severity of out-of-trueness. I detected a very slight wobble, with the rim moving away from my brake shoe by maybe 1 mm at the farthest point, where it was just barely touching at the closest point. Is this enough to be worth correcting, or should I look elsewhere for the source of my front oscillation?