It would be nice if they archived to film. However, if the originals are on magnetic tape ("video" archive), then digital is a step up in some ways (so long as they run the expensive hamster wheel of backups and upgrades). Magnetic tapes "fade."
Could be the TV settings. I've never seen problems like that with analog movies at the theatre - there is an whole persistence of vision thing that has something to do with frame-rates; so stutter is likely not the frame-rate itself. I believe TVs use 29 or 30 fps (regardless of what the original used) - at least in the States (NTSC).
On the other hand, I've seen problems on DVDs of old movies. During the opening scene of It's a Mad Mad Mad Mad World, my friends were enjoying it while I instead noticed all the combing and pixelation.
I picked up an old broken Laserdisc player hoping to play with the laser. It was 2nd generation and had a solid state laser
- so I fixed it instead and got some old discs. I was very surprized with the ocean scenes in Hunt for Red October - absolutely flawless, no artifacts at all. Then again, Laserdiscs were analogue (FM modulation, I believe).