Does Multibit Merchant offer any solution(s) for this problem or does the owner of the webshop get there bitcoins and still needs to go to an exchange and trade there bitcoins for euros/dollars/pounds?
(I'm the lead developer for MultiBit Merchant)
As part of my October of Bitcoin I'll be pushing MultiBit Merchant to a minimum viable product (MVP). This means that I have to strip out as much extraneous work as possible to hit that tight deadline. The MVP is unlikely to have automated fiat exchange in place, although prices will be quoted in real time from MtGox in a range of local currencies.
However, I am also involved with the XChange project and as part of that there is a push to introduce a Deposit/Withdraw API in addition to the trading API. Using XChange it should be possible to take bitcoins, deposit them onto the exchange offering the best deal at your market depth (arbitrage) and perform a trade to fiat. That fiat can then be withdrawn to your selected account using the exchange's provided mechanisms.
XChange is a Java library, but because it runs on the JVM (now known as the mlvm) it is possible for it to be accessed by any other language running on the technology (think Clojure, Jython, JRuby etc). In time, this will make it trivial for anyone using the mlvm to be able to interoperate with a wide range of exchanges.