I think I would be worried about the engine running on low oil pressure.

If they left the oil filter loose the oil would be coming out at pressure say 60 PSI and that accounts for it being all over the place.
What damage could have been done to the engine?

Imagine if you went a long drive after having it serviced and the power steering belt had not broken.
It's a good chance all of the oil would have left the engine before the oil pressure light would have come on.
The thing with oil pressure sensors are they are set very low.