I never use "J" boxes if at all possible to omit them. There is no reason for them in this plan.
4-way switches are used when there are more than 2 switching locations, but the first and last switch in such a run are 3-way switches.
The number of conductors between 4-way switches is three, not 4 as shown, but then the switching sequence is not really indicated. Maybe this wiring is required.
I would not have quite so many switches as shown, and I would place them differently. It is customary to indicate with lower case letters (a,b,c) which light fixtures are associated with which switches.
