So far the only times this has happened was when I grab new things from the add parts sections and then I can no longer move things, only make them highlighted
I've tried spamming alt tab, grabbing things out of the new tab. but I cant recreate it.
{update}
it has something to do with the shift-+tab that steam does after uploading an aircraft, then exiting.
Here
Skip to around 40 seconds
Steps to repro:
Hold left shift
Hold down left mouse button and drag
Press Tab
Let go of shift and mouse button
Click "Click Here to Return to Game"
You can no longer move parts with left click.
Workaround: Just press and release left shift and the game will start working normally again.