https://fred.stlouisfed.org/graph/?g=1Mc3z

Manufacturing and mining are becoming much less correlated to the overall jobs market (likely, as you point out, b/c the government smooths the other sectors).

https://fred.stlouisfed.org/graph/?g=1Mc3I

This is despite being a relatively flat % of employment since 2010 (after a long period of decline).

https://fred.stlouisfed.org/graph/?g=1Mc4f

As mentioned, there is also the weirdness of SWE's going from 'better than the overall market' to 'worse than the overall market'.

https://fred.stlouisfed.org/graph/?g=1Mcer

Retail employment is also dislocating.

Those are just the examples I can think of with no research, I'm sure there are others.