Does your screen resolution change during the login process, or from when you logged out to logging back in?

No.

Which type of panels are you using? Default/Empty or Grouping?

Default, at the top of the screen.

Does the messing up still occur if your panel is in other locations, such as on the sides or bottom of the screen?

Haven't tried that, but seemingly tamed it by dragging these applets to other side of the Task Manager: Digital Clock, Show Desktop, Textmon and CPUtemp.

Okay, that hints that it may be the initial sizing of applets which is causing this.

As I have never seen this behaviour before, chances are the developers have not either. This makes it extremely difficult for them to fix it. Can anyone else reproduce gnomeshellhater's observations?

The problem comes around when you leave blank spaces in your panels. Remove anything you don't want, then add a panel spacer to fill in any gaps. That's how I solved my problem.

If others can confirm that this indeed fixes the issue, please add this information to the bug report so the developers can investigate more closely and apply the relevant fixes.

Same Problem in Manjaro KDE, Linux Mint 18 KDE, KDE Neon and now in Kubuntu 17.
Seriously frustrating and so much work to always set up new System. This stops me from being able to properly work with KDE Plasma.

Any progress on this bug within the last 4 years? (since latest post)

so apparently adding a spacer seems to be the fix. i had the same problem in manjaro and it got fixed just by adding a spacer in between my widgets on the panel.
before that, the widgets just kept getting messed up every time i logged in. weird how this hasn't been fixed all this time

You do realise you are in a completely unrelated post about Plasma 4 from 8 years ago, while you are very likely using Plasma 5...

Please do NOT comment on threads that are clearly outdated and, like in this case, likely totally unrelated to your problem (different codebase and Qt version to start with...)
Locking topic.