Wow..... That's really shoddy workmanship, very very poor.

I'm guessing that the place you took it too understands how a diff works, and especially a Limited Slip Diff.....Coz it don't look like it

A good amateur mechanic should have been able to strip and and rebuild it in a couple of hours.

I know how you feel, but for the sake of time.... It might be just worth you getting a seal, checking the torque settings of the diff, and putting it back in yourself....Otherwise I'm sure they'll have it for another week, and at the end of the day, what will the workmanship be like !!!!

This should definately be a Name And Shame !!!!