I'm lucky enough to be able to pay cash for a condo I'm buying
($400K).  However, I'm wondering if it makes sense to take out a
mortgage anyway for $200K.  Factors: not sure how long I will live
here...could by as little as 1 year, but likely to be more. My thought
was to get a 3/1 ARM mortgage, so that if rates jump, I can just
prepay.

I figure that I can borrow for about 4%, and probably do better than
that with investments.  But, I'm just not sure that with closing
costs, etc, that it might just not be financially worth the hassle of
taking out a loan.  Assume that the financial issues are the only ones
that matter to me.

Pay cash!

Investments can and do go down & I only heard this week of man in
London (UK) who mortgaged his flat for £200,000 and then lost it all
in the Dot Com crash.

And this same man had been bankrupted in 1987 by a can't miss Stock
Exchange investment opportunity.

And this guy, who is now turned 70, has had to go back to work.

It depends.  The 4% loan really costs less than 4% if you are in a
country that allows you to deduct the mortgage interest from your
taxes. (eg the US)  So if you are in the25% tax bracket then the money
costs you 3%.  You can probably find some reasonable investments with
safety that can net you close to 3%.(bonds)  It depends upon such
factors like:
1. How liquid do you need the 400K to be?  It isn't too liquid tied up
in a home, although one can borrow against the equity in the home.

2. Do you have other sources of income and don't need to rely on the
400K being in the bank? (you lucky dog!  Do you want to adapt a son? 
I can call every day and say nice things. :-) )

3.How risk adverse are you with regards to money?  Perhaps a 200K
mortgage is a good idea and invest the rest in a stock index fund or a
bond fund or bank CDs.  Interest rates are moving up so locking in a
rate for debt might be a good idea - especially if we have inflation
where the home will appreciate and the cost for the home will
decrease.  Short term bonds or money markets will ride the interest
rates up; even inflation adjusted US Treasures might be a good idea -
lock in a safe rate of interest and protect from inflation.

4. Your financial situation.

These and many more are all things you will need to determine for
yourself.  I'm not an investment advisor - just a computer nerd - and
I can't tell you what would be a good course of action.  Best wishes.