I accidentally deleted my system tray from the panel on KDE. When I added it back, it and the clock are now left aligned in the panel instead of right-aligned like they used to be. Dragging them back to the right does nothing, they pop back left as soon as I lift up on the mouse. I want these right-aligned. How do I fix this?

When you go to the panel settings you have an "Add Spacer" button. This is used to push widgets to the right side. Just put it in the correct place and both system tray and clock should end up pushed to the right side.

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Right-click on the panel and select Panel Options-->Panel Settings. When you hover over a panel widget, a little dialog with a wrench on the left (configuration) and an X on the right (delete widget) should appear. Click-and-hold that dialog and you should be able to re-position the widgets to your liking.

Yes, that's what I've been trying, but whenever I reposition they just pop back to the left!
Tried that, but not very satisfying. I've got to extend the spacer from the quick-launch items on the left all the way to the right to push the system tray stuff as far right as I can. I'm concerned what might happen to new quick-launch items I add in the future.

In the end, I simply deleted the panel, re-added the default panel, reconfigured my clock, removed some system-tray items and added back my quick-launch selections. Took less time than writing this post!

Thanks for helping.

That's no problem. The spacer is flexible. If the quicklaunch grows (or the system tray for that matter), the spacer will simply shrink. It will also grow again, if the quicklaunch (or the system tray) get smaller again.

Either way, good that you got it working again