Mealy bugs on one (so far) of my orchids
 

I noticed what looked like cobwebs on one of my dendrobium a few days ago, but didn't think much of it at the time. Today I looked closer and saw that it was the sticky substance from what I think are mealy bugs. This is one of the plants I've had the longest and it's kept a in the middle of most of my plants. I removed the bugs I could see. I was worried one fell into a neighboring schomburgkia so I took that and the dendrobium and sprayed them both down with neem oil. I plan to keep them isolated for a bit and see how they do.

I'm wondering...is neem oil sufficient and do I need to treat all my plants? Also, should I be repotting? I want to get ahead of this now and am hoping not to lose plants.

Webbing might mean spidermites. Neem oil should take care of them. You should spray all of your plants well and treat a few times to make certain you get them all. Good luck!

They're kind of flat, whitish, slightly fuzzy looking bugs with almost a plated appearance.

Leafmite was right, spiderweb-like appearance is normally associated with spidermites, but the bugs you're describing do sound like like mealy bugs. If they are just on one plant you can isolate it and zap the mealies with a Q-tip dipped in isopropyl alcohol. Just dab them with the Q-tip. This needs to be done daily so it's labor intensive and continued until you see no more mealy bugs. I would resort to chemical warfare if you begin to see the infestation spread to other plants.

My response is, spray the plant with a systemic. I like imacloporid. Then, water it with the same dose as mealy bugs hid in the media.
Repeat in 2 weeks.

You can try with more natural techniques but all too often that results in a persistant problem.