Holy crap, the same thing is happening to mine!!! It was gorgeous earlier, but it's got the same thing! I have two other honeysuckles that are doing fine...

Sounds like Powdery Mildew. There are a number of cultivars that are prone to it. Last year my Goldflame was covered in it as well as my peony. This year it seems to be okay. The weather often plays a factor in how bad it will be that year. You can spray with anything labeled for PM or try the Cornell formula as a spray (or equivalent which I think is baking soda in water with some Ultrafine Horticultural oil and Murphy's oil soap as a sticker).

My two Honeysuckles used to have the same problem until I learned that the aphids which overwinter on the vines cause the black gunk which in turn causes the fungal diseases such as mildew etc. Now I dormant oil spray mine every year before the leaves break out and I never have a problem now.

Mine developed the powdery mildew the first year. Then I read somewhere that spraying a solution of 50% water with 50% non-fat milk would control powdery mildew and it worked like a miracle!

Now suddenly it's leave are yellowed and spotted. I assumed at first it was the mildew again, but upon closer inspection saw there are 1/8 inch wide "trails" through the leaves, as if some kind of insect has tunneled through them. But when I looked on the backside of the leaves there's no evidence of the trails.

Anyone have a clue what kind of bug would do this and what to do to control them?