I am thinking of starting a news stand and I am considering allowing
someone to buy a magazine (say 'Newsweek') at regular price and then
if they return it to me aftre reading it I will give them 50% $ back. 
I want to then turn around and allow a second person to purchase that
same copy of the magazine for full price and if they return it give
them 50% back.  In a sense, renting the magazine to multiple people.

Are there any legal issues with this approach?

If it isn't, it should be.  It is sort of like music file swapping. 
Each rental of the magazine is money taken from the pocket of the
publisher.  Instead of three or four people actually buying the
magazine, only one will but three or four people will read it and
still pay the full price for doing so if they don't bring it back. 
they will still pay for readint it if they do bring it back.  In my
personal opinion (which I realize does not mean much), such an
activity would be nothing less than theft from the publisher.

There is also the health aspect to consider.  In as much as many
diseases such as the cold and flu are spread by hand contact with
objects where the viruses, etc, are present, a magazine first sold to
a person who had a communicable disease could in turn infect many
more.

Not really a good idea.

digs

Same issues digsalot mentions apply to libraries as well, though not for profit.

I respectfully disagree with Digsalot-ga.  I see no legal impediment
as long as you don't have a contractual obligation with the magazine
supplier not to rent it out, or as long as magazine publishers don't
"license" their magazines for single-person use.  It is advertising
that pays for magazines, and the ads are sold on the basis that there
are X readers per printed issue.  If such renting became widespread, X
would increase, and so would advertising rates to make up for it.

Yeah, I have to disagree with digsalot also, as the fileswapping
analogy really breaks down here.  Firstly, there is the fact that the
physical object is being traded, not a digital copy.  Second,
libraries already do essentially the same thing with no charge, so how
on earth could it be illegal to simply charge for the service.  This
is more similar to a used book store that maintains an exchange policy
as well.

On a separate note, I can't see how this would succeed as a business
though for several reasons.  First, readers of a news magazine aren't
going to want a week old edition, so you are going to have a whole lot
of unwanted used copies if you try to sell last week's copy at the
same price as this week's.  Second, people who read these things
regularly are going to have subscriptions by and large and pay much,
much less than the cover price in the first place.

Addendum to leo's comment: I have seen this work in Africa, where news
is not necessarily current, where ANY news may be valued.  And regular
readers do not always have the means to buy a subscription, to pay 12
months (or whatever) up-front, and prefer to pay, copy by copy.

But jmh might consider a sliding scale for his entrepreneurship, which
takes into account the diminishing value of the magazine.  Thus the
first reader pays full (?) price for the magazine, and gets 50% back
on return, reader number 2 pays 75% of the original price, and gets
50% of the price paid on return, reader number 3 pays 50% of the
original price, and gets 50% of that 50% repaid...

It may not be profit-making, but if jmh gets first read of the
magazine, then any additional reader cuts the cost of his reading.  Of
course, that only works if he stocks the news-stand with single
copies.

I don't see any legal issues here, single or multiple copies.  If
there were, then any and every second-hand bookshop, comic store etc
would be trading illegally.  They aren't, they are asking whatever
price they think the market will bear, what the reader is prepared to
pay.  And if the reader is prepared to pay full-price (or more for a
rare magazine), then so be it.

The only resale restriction might be if you change the cover or the
contents in some way;  I am thinking here of books which often have
(had?) some restrictions on re-binding or re-covering.

I would offer this as an answer, but I am not a lawyer (so note the
disclaimer at the bottom of the Google Answers page) and I haven't
found anything at a quick glance to support my case.  Nor anything
against it!   (But I'll be happy to post this as an answer if
pressed.)

Good luck (but don't expect to get rich on this...), r2l.

For several years I worked in a used book store. In addition to books,
we sold used magazines for a fraction of their cover price (much less
than half).

It was not unusual for the same magazine to be sold, returned for
credit, and sold again, sometimes more than once in the same day. Many
used books stores do this. I can't comment on the legality in all
jurisdictions, but this seems to be perfectly legal in Oklahoma, where
I live. One of our best customers was a cop who came in often to get
magazines. I doubt that he would have done this if he'd been breaking
the law. Such a law would presumably put used book dealers out of
business.

Hello again,

I've got a little further with this question.  It's certainly
intriguing.

It may come down to a matter of which magazines you are planning to
rent or re-sell, where they are published, and how and from whom you
purchase them yourself, and of course where you intend to set up your
news-stand may make a difference as well.

So if you can give us guidance on these issues we might be able to
give you a more definite (layman's) opinion.

best, r2l