All members of a shared folder have full read and write privileges. Setting read-only permissions isn't currently possible, but the feature is on Dropbox's roadmap.
If you're interested in sharing files for people to view or download only (i.e. read-only access), consider getting a link to a file or folder instead of creating a shared folder.
Some permissions systems are incompatible between operating systems. For example, a file with read-only access on your Windows computer may not be protected on your Mac. Dropbox doesn't change a file's permissions when syncing, but can't guarantee the permissions you set in one operating system will work properly when opened from another computer.