Looking to upgrade from Mojave to Monterey.
Should I expect any issues doing this as it is a version 3 steps higher?
Or would it be better upgrading one version at a time?

Prob. not, but a three version upgrade is a pretty big step. Safer to do one step at a time, I think. Double-check that your Mac is supported by the eventual target version, macOS will gracefully decline to install on "old" hardware, so there is little risk, but it can be time consuming and frustrating to find the limits.

Just make sure you have a clean time machine backup before starting..

PS - the jump should be fine.

Last time I updated the OS on my MacBook Pro, I get this message many, many times a day:

“owncloud” is damaged and can’t be opened. You should move it to the Trash."

I can still access all of it no prob. But what a pain in the ass.

 
I made the same transition. Just make sure to have a good backup of your Mojave install and you can use Migration Assistant to move almost all of your Applications, files and settings. Time Machine can get messy. I prefer to use Carbon Copy Cloner to create a one-time .dmg image of the old system, mount that, and use Migration Assistant to restore it.

OK, did the upgrade from Mojave to Monterey direct.
No problems that I'm aware of. All App's working as before.
Now I have to learn all the things that are different or new.