Space Station, gyrodyne problems. Hubble, gyrodyne problems, most critical
item that limits the time between service missions. Any other NASA
spacecraft with gyrodyne problems?

As far as I know, Hubble's reaction wheels and magnetotorquers are
working fine (it doesn't have gyrodynes).
(reaction wheel - spin slower or faster, for rotation along a single
axis per wheel
magnetotorquer - work against the Earth's magnetic field
gyrodyne - a wheel whose axis is turned, analogous to the high school
physics bicycle wheel demo
)

What has been a problem on Hubble is the gyroscopes (i.e. sensors).
Other spacecraft too. The irony here of course is that there are
replacements with no moving parts (e.g. fiber optic gyros), but said
replacements aren't yet as good as the traditional moving gyroscope.
Someone is working on one which could replace the moving gyroscopes
for spacecraft - if memory serves it was some kind of vibrating
gyroscope shaped a bit like a wine glass.
Here's a gyroscope taxonomy: http://www.spp.co.jp/sssj/sindoue.html