I removed world read/execute permissions from /proc and I can't see that it broke anything, so far.
Why is /proc world readable by default? I don't want shell users snooping around in there.
Er, why not? What are you hoping to stop them seeing? The /proc directory is there for programs, especially scripts, to see what the system is doing. All the world readable information in there would be available via the system API at the C level anyway, so you haven't closed what you perceive to be a security hole.
The stuff in /proc which shouldn't be seen by regular users is protected by read/write permissions already: try looking at the contents of a directory which represents a process you don't own.
I would suggest you put it back. There's not much that uses /proc that you might use on a day to day basis, but you're going to hit some pretty weird errors sooner or later.
ps uses it..