Why won't Dropbox sync particular files on my mac?

The HFS+ filesystem includes flags, which provide extra permissions on top of the usual Unix permissions. One of the flags is "unchangeable" - which does what the name suggests.

Several files inside my dropbox had been flagged as unchangeable. You can check for this with ls:

Sombrero:directory polleyj$ ls -Ol
total 0
-rwxrwxrwx  1 polleyj  admin  uchg 0 15 Jan 23:29 file1

-0 tells ls to show the extra flags; uchg indicates that this files in unchangeable.

Sombrero:directory polleyj$ rm file1 
override rwxrwxrwx  polleyj/admin uchg for file1? y
rm: file1: Operation not permitted
Sombrero:directory polleyj$ mv file1 ..
mv: rename file1 to ../file1: Operation not permitted
Sombrero:directory polleyj$ 

To fix this, use chflags:

Sombrero:directory polleyj$ chflags nouchg file1 
Sombrero:directory polleyj$ rm file1 
Sombrero:directory polleyj$ ls
Sombrero:directory polleyj$