When a machine is moved to a new spot via the picker dollies mod, the indicator light doesn't move with it. It stays in the old spot.

This happens to me too!

yes it's very annoying to see such pictures. even save load don't fix lights https://puu.sh/GwTlH/93e649f781.png
in factorio 0.17 version everything was fine - lights move with building. i think it was some 'performance improvement' in later versions...

After some debugging, found the issue. Looks like a regression in the Picker Dollies mod.
Fix:
1. Unzip the Picker Dollies mod.
2. Open up controls.lua in a text editor.
3. Add the following line below the other requires at the top of the file:
'local interface = require('interface')'
4. Save the file and rezip the extracted mod folder.

thank you!