Uhh...yeah.
Anyway....
...according to several links I have seen, the average hours worked in a part time job is about 20 hours per week (not official numbers).
Here is an EU link:
Eurostat - Tables, Graphs and Maps Interface (TGM) table
If that is the case here, then that would mean that 523,000 jobs at a minimum of 35 hours per week are being replaced by 799,000 jobs at roughly 20 hours per week.
523,000 times 35 = 18,305,000
799,000 times 20 = 15,980,000
So, this would mean that there were less hours worked each week then the previous month...despite the fact there were more jobs.
In fact, by my math, you would need 22.9 hours per week per part time job just to equal the number of hours lost due to the demise of 523,000 full time jobs.
Also, the full time number was a theoretical minimum (based on evey job lost being equal to a maximum of 35 hours per week) that will certainly be much higher in reality.
So, on the face of it, not only is this jobs report not nearly as good as the headline suggests - it may even be a net regression of total employment hours available to Americans in June over May.