Seems like every time I manage / edit block it breaks something. At first I thought it was my theme, but it doesn't seem to matter. It's getting to the point where I am afraid to make any changes because its going to break something.

This does seem restricted to either your site or server setup. I haven't seen or heard of this before.

What sort of server are you running on? Shared, vps or dedicated?

Are you running a cache. Me personally. I had nothing but issues with APC on my vps. So i went with memcache with database files in the admin settings, and using cloudflare free.