File Syncing

[dads]

I've created a small application that when you click one of the
buttons it randomly picks a paragraphs from a list that it generates
from a text file and then copies them to the clipboard. It also has
make new/edit/delete/print/ etc functionality.

It's for work so I get some brownie points and every know and then I
could work on it and learn python while getting paid (heaven) instead
of my normal customer service job (mind I've done 95% of it at home).
I've been allowed to install it on one of the blade servers so one of
the team can use if they connect to that server. Great stuff.

When we normally connect through one of the thin clients we connect
randomly to one of three blade servers. I've just thought that when I
add the app to the other servers they will be completely separate. So
if the the paragraphs which are stored in text files are amended/
deleted/created will only happen on one server and not them all. I've
a couple of questions:

What would happen if more than one person used my application at the
same time? I haven't added any I/O exception code so I think that
would be an issue but would python crash? (it's only got simple
functions and controls in it, no threading or process code or anything
like that, i'd post it but it's 2500lines long)

What would I have to learn to be able to sync the text files on each
server? python network programming? Or something else? Sorry for my
naivety =p