OSX Server 10.9 File Sharing - not working properly
If it's the group ownerships, from the command line you could do:

chown -R yourusername:staff /Path/To/SharedFolder


for each of the shares, if the other non-admin users you mentioned are in the staff group. Otherwise, replace staff with the correct group. It's possible you may not want all the directories underneath the shared directory shared, so you'd have to go in and alter the permissions/ownership for each of them too, or remove the -R and change folders individually.

See some examples of chown here and an explanation of the command I've given here.

I'd also note down what the current ownership and permissions are using ls -l, so that you can change them back if this doesn't work.

(obviously, replace yourusername with your username, and /Path/To/SharedFolder with the path to the shared folder. I say "obviously" but I'm writing this because, according to my experience, it's not always obvious!:)