I just opened my brother's old high school dudley lock, with no prior knowledge of the combination.
I believe the vulnerability is related to a flaw in the manufacturing process, where the wheels are not of identical size.
For reference, my lock has a black dial, the 'all-capital-letters' DUDLEY logo, and has a 'B' printed on the back.
The method I used:
I started dialing pairs of numbers, starting from
0-55, 0-52, 0-49 ...
3-58, 3-55, 3-52 ...
etc., and pulling on the shackle at each combination to see if it got harder to move (I moved the dial back a few digits before pulling and wiggling it, so I wouldn't screw up the second number).
The dial moved freely in most combinations, with one exception: whenever the second number was ~21, the dial (third wheel) would encounter resistance whenever the shackle was pulled, in all gates except for one, between 5 and 8.
Since I was going right from 0, I found this behavior was consistent for combinations 7-21, 10-21, 13-21, 16-21. Because a number like 19-21 is awkward to dial (the buttons that connect the dials are ~3 "digits" wide.
After I imagined the innards of the lock, I realized that the second number must be ~21, and the third number lay in the 5-8 gate. I went back to 0 where I started from, and started dialing full combinations, but moving the first number left instead of right.. The second combination I got to worked perfectly: 54-21-7 (or 55-20-7, as it's easier to remember

)
I noticed that when dialing the combinations (55 through 20)-20-xx, the dial got rigid ("scratchy") as I mentioned above.
When dialing (20 through 55)-20-xx, the dial didn't get too much more difficult to move, but seemed to squeak a little louder than usual.. although I may have imagined it.
My best explanation for this magical method is that the wheels inside must be of slightly different diameters and not perfectly circular (and/or not properly centered). When pulling on the shackle, you will lock one of the three wheels (the one that has the biggest diameter at that particular point). On most Dudley locks that I have seen, the front (third) wheel -- the one with all the gates -- is not the biggest, and rotates freely almost all the time (restricted only by its false gates).
I believe in my case, the third (first number) was the smallest, the front wheel (third number) was a little bigger, and the second wheel was the biggest. When the second wheel was dialed correctly, pulling the shackle locked the front wheel (connected to the dial), and provided tactile feedback, UNLESS it was pointed to the real gate. In one part of the circle (NOT the one I tried first

, the third wheel was bigger than the second (due to lopsidedness or bad centering), so the front wheel never locked up, even if the second wheel/number was dialed correctly.
Some notes:
1). The second and third wheels have one false gate each, so you may end up narrowing them down to a total of 4 possibilities, of which one is correct
2). Dialing pairs of numbers is extremely fast: dial the first number, loop around to pick up the second wheel, and then edge it along 3 notches at a time.. no need to reset and redial the first number until you're done with it... this is a really fast to do, and even if you try the correct combination last of all after running into every false gate, you'll still be done in a reasonable time (I don't see it taking more than half an hour, ever).
I hope that wasn't too wordy for my first post, but I really believe that this is the simplest way of decoding this type of lock, and I hope that I envisioned its inner workings correctly (pros, please correct me if I am mistaken about something). Stray's way of putting a feeler through the shackle and feeling the wheels inside is faster and cooler, but much harder I think: the shackle fits very snugly in the hole so you need a really thin feeler and some practice at the very least -- at least, I wasn't able to do it:)