If you've recently moved to a new address within the same state, different than the one specified on your driver's license, will it create any problem when purchasing a firearm from a dealer, assuming you notify them of your current address?

Technically you are supposed to be able to prove where you reside.  Most FFLs these days take that to mean that the address on your I.D. must match your current residence.  There are other acceptable combinations of paperwork, but most FFLs don't like the hassle and incrementally greater chance of messing up and incurring the BATFE's wrath.

Best bet is to head down to DMV and get the license updated/replaced.

Also, you can always check www.atf.gov/firearms/faq/index.htm for answers to questions like these.

Futuristic

"...recently moved..."

Most, if not all, states have laws that require you to change your license address within a short time period, like 7 days.

"...will it create any problem..."

Not only may you not be able to purchase, you may get a ticket anywhere you drive.

PK90, sounds like they treat you Yanks a little different than us hillbillies.  I found this from our DMV website:

How can I update the address on my Missouri Driver License?
If you want to update the actual driver license card that you carry in your wallet, you must apply and pay for an updated license at a Missouri driver license office. If you are within six months of the expiration date on your driver license, you may apply for an early renewal. If not, the transaction would be processed as a duplicate with the same expiration date as your current driver license.

Regardless of whether or not you choose to update your actual driver license, please send an email message including your full name, Missouri driver license number (or social security number), the vehicle license plate numbers of any vehicle(s) you have registered in Missouri, and your old and new mailing addresses (including the name of the county) to [email protected]. Our staff will then forward your address change information to the appropriate driver license, motor vehicle, and taxation staff.

So basically it says you only have to if you choose.  Guy at my gunshop just says to bring in a document that shows proof of new residence.