I had a funny buzzing maybe a whirrrring noise coming from the front end of my '03 ultra. i got home and did some checking and found that the nuts holding the front axle cap had come loose. What other "Critical fasteners" should I be looking at that could work loose?

 

Engine mounts and any bolt,nut,screw you can find!

 

Suggestion: Buy the HD Service Manual for your bike. It will identify what HD considers to be the "critical fasteners" AND give your the torque specs for them. My '04 SM identifies the axle, brake, front forks, hand control, handlebar, and pivot shaft fasteners as the "critical fasteners."
Knowing which fasteners are "critical fasteners" is one-half the answer; the rest is knowing what torque value to tighten them to for the job to be done right.

As a previous poster said, check them all; for example, when you do a thorough detailing job on the bike.

 

I do have a service manual for the bike, got it from one of the forum members here and I have scanned that particular section. I just thought I'd ask anyway, some folks may have experienced things not covered in the book. Good idea though to check any of'em I can get my hands on.