Do you have a bit more info about your system?
What Windows version are you using?
What hardware are you using?
Does this happen with JJ2+ aswell?

Max FPS for the original client was 70 fps and for the JJ2+ addon 120 fps.

My specs are:
Windows 10
i5 4670k 3.4ghz
GTX1080 8GB
24 GB Ram

I'm getting the same performance using JJ2+. I even tried using a DirectDraw wrapper that I found on the JJ2 forums, but that just made the game worse.

It feels like everything else is smooth except for the scrolling. For all I know, the game is probably fine. It might just be a quirk of the game's engine, but then again, it might not be. I did notice the scrolling was jittery watching videos of the game last night, but it's hard to truly tell. I wonder if this game would look smoother on a PC monitor, seeing as that's what it was designed for. This wasn't a game I grew up playing (unlike the original) so I have no memories or recollections to base my impressions off of.

Using Vsync? try going into nvidia control panel and turn pre rendered frames to default to program or 1 sometimes that fixes the issue like it did for me for some other games. Hope that helps.

I was experiencing the same problems. After some fiddling around with the options I was able to get it working correctly by disabling "Hardware Mode" in Options -> Video -> Advanced.
Hope this helps :-)

The option for Hardware Mode is greyed out on my machine and defaults to off, and I don't know how to activate it. I understand that the game prefers software mode since certain effects are only available in that mode, but I'd like to see if hardware mode makes any difference in my case. Is there any way I can activate it outside of the game?

JJ2+ dropped support for Hardware Acceleration with possible plans of restoring it in the future. It's unlikely that it would fix your issue, but if you wish to give it a try without disabling JJ2+, you can use one of our archived releases. If I'm not mistaken, 2013-02-05 should still support Hardware Acceleration.

Another one here with the jittery scrolling. Hardware mode is an absolute no-no - makes it at least twice as bad. Even with software mode, it's still quite choppy. JJ2+ doesn't run any smoother either.

Can anyone who played this game on old systems back when it was first released, please confirm whether or not this is how the game is supposed to be.

I'm using Windows 8.1 by the way, if that matters.

The old PCI-Cards (Matrox/Voodoo3/Nvidia up to Riva128) and the intel igp's up to 845gv/865g do support the hardwaremode, but only in 640x400 at 8Bit. With this the game is gorgeously smooth.

All later stuff does not support the hardwaremode at 640x400, they do all produce jittery scrolling no matter what option you choose. The native MacOS Version does also have no stutterfree-scrolling. So the best way seems to be having an old pc with an old gfx-card.

It's a sad thing that my MacMini CoreDuo GMA950 also does not support the stutterfree scrolling :(

Yep, I even tried Nvidia Inspector and Microsoft Compatibility Toolkit fixes suggested in another thread and it seemed to make little/no difference. It feels a little less stuttery, and the FPS counter is locked at 60, but the background definitely stutters somewhat, unlike the smooth experience I had playing in Hardware Mode back in the day. At least it's still very playable, just not quite as smooth as it should be.

I can't promise you that my way will work for you, but give it a try:
Be aware: I am on a Vega 64 running a 2560x1440 Monitor which is capable of 144Hz. I run Jazz2 at 800x600 16bit 120Hz which ist perfectly smooth. As it might be that your Monitor can't Handle my Resolution or Hz, you might need to change these Settings.

1.) download dgVoodoo 2.62.3 (latest stable version as I am writing this).
2.) copy all the dgVoodoo Stuff into the Jazz2 Folder
3.) copy all the DLLs from the \MS\x86 Folder into you Jazz2 Folder
4.) Configure dgVoodoo as in the attached Picture*

*for some reason I can't post my dgVoodoo.conf. It wont safe the Post or the Edit of the Post for ages...

I forgot to mention the power plan. As long as you keep the power plan at "balanced" you might get stutter and wonky fps. Give "high power" a try to get perfect stable fps. Jazz2 doesn't need the power, but your system wants to fall to sleep constantly. ;)